ClearBridge Energy Midstream Opportunity Fund (EMO) N-CSRSCertified semi-annual shareholder report (management investment company)

CLEARBRIDGE

ENERGY MIDSTREAM OPPORTUNITY FUND

INC. (EMO)

Fund objective

The Fund’s investment objective is to provide long-term investors a high level of total return with an emphasis on cash distributions.

The Fund seeks to achieve its objective by investing primarily in energy midstream entities.

Letter from the chairman

Dear Shareholder,

We are pleased to provide the semi-annual report of ClearBridge Energy Midstream Opportunity Fund Inc. for the six-month reporting period ended May 31, 2021. Please read on for Fund performance information during the Fund’s reporting period.

As always, we remain committed to providing you with excellent service and a full spectrum of investment choices. We also remain committed to supplementing the support you receive from your financial advisor. One way we accomplish this is through our website, www.lmcef.com. Here you can gain immediate access to market and investment information, including:

We look forward to helping you meet your financial goals.

Sincerely,

Jane Trust, CFA

Chairman, President and Chief Executive Officer

June 30, 2021

Performance review

For the six months ended May 31, 2021, ClearBridge Energy Midstream Opportunity Fund Inc. returned 59.87% based on its net asset value (“NAV”)ⁱ and 80.38% based on its New York Stock Exchange (“NYSE”) market price per share. The Alerian MLP Indexⁱⁱ and the Lipper Energy MLP Closed-End Funds Category Averageⁱⁱⁱ returned 44.09% and 43.86%, respectively, over the same time frame. Please note that Lipper performance returns are based on each fund’s NAV.

During this six-month period, the Fund made distributions to shareholders totaling $0.71 per share. As of May 31, 2021, the Fund estimates that all of the distributions constituted a return of capital.* The performance table shows the Fund’s six-month total return based on its NAV and market price as of May 31, 2021. Past performance is no guarantee of future results.

All figures represent past performance and are not a guarantee of future results. Performance figures for periods shorter than one year represent cumulative figures and are not annualized.

** Total returns are based on changes in NAV or market price, respectively. Returns reflect the deduction of all Fund expenses, including management fees, operating expenses, and other Fund expenses. Returns do not reflect the deduction of brokerage commissions or taxes that investors may pay on distributions or the sale of shares.

† Total return assumes the reinvestment of all distributions, including returns of capital, if any, at NAV.

‡ Total return assumes the reinvestment of all distributions, including returns of capital, if any, in additional shares in accordance with the Fund’s Dividend Reinvestment Plan.

Looking for additional information?

The Fund is traded under the symbol “EMO” and its closing market price is available in most newspapers under the NYSE listings. The daily NAV is available online under the symbol “XEMOX” on most financial websites. Barron’s and The Wall Street Journal’s Monday edition both carry closed-end fund tables that provide additional information. In addition, the Fund issues a monthly press release that can be found on most major financial websites as well as www.lmcef.com (click on the name of the fund).

Performance review (cont’d)

In a continuing effort to provide information concerning the Fund, shareholders may call 1-888-777-0102 (toll free), Monday through Friday from 8:00 a.m. to 5:30 p.m. Eastern Time, for the Fund’s current NAV, market price and other information.

Thank you for your investment in ClearBridge Energy Midstream Opportunity Fund Inc. As always, we appreciate that you have chosen us to manage your assets and we remain focused on achieving the Fund’s investment goals.

Sincerely,

Jane Trust, CFA

Chairman, President and Chief Executive Officer

June 30, 2021

RISKS: The Fund is a non-diversified, closed-end management investment company designed primarily as a long-term investment and not as a trading vehicle. The Fund is not intended to be a complete investment program and, due to the uncertainty inherent in all investments, there can be no assurance that the Fund will achieve its investment objective. The Fund’s common stock is traded on the New York Stock Exchange. Similar to stocks, the Fund’s share price will fluctuate with market conditions and, at the time of sale, may be worth more or less than the original investment. Shares of closed-end funds often trade at a discount to their net asset value. Because the Fund is non-diversified, it may be more susceptible to economic, political or regulatory events than a diversified fund. The Fund’s investments are subject to a number of risks such as stock market risk, MLP and midstream entities risk, market events risk and portfolio management risk. MLP distributions are not guaranteed and there is no assurance that all distributions will be tax deferred. Investments in MLP securities and midstream entities are subject to unique risks. The Fund’s concentration of investments in energy-related MLPs and midstream entities subjects it to the risks of MLPs, midstream entities and the energy sector, including the risks of declines in energy or commodity prices, decreases in energy demand, adverse weather conditions, natural or other disasters, changes in government regulation, and changes in tax laws. Leverage may result in greater volatility of NAV and the market price of common shares, and increases a shareholder’s risk of loss. The Fund may make significant investments in derivative instruments. Derivative instruments can be illiquid, may disproportionately increase losses, and have a potentially large impact on Fund performance. The Fund may invest in small-capitalization or illiquid securities, which can increase the risk and volatility of the Fund. The Fund may also invest in money market funds, including funds affiliated with the Fund’s manager and subadviser.

All investments are subject to risk including the possible loss of principal. Past performance is no guarantee of future results. All index performance reflects no deduction for fees, expenses or taxes. Please note that an investor cannot invest directly in an index.

Fund at a glance^† (unaudited)

Investment breakdown (%) as a percent of total investments

Schedule of investments (unaudited)

May 31, 2021

ClearBridge Energy Midstream Opportunity Fund Inc.

See Notes to Financial Statements.

ClearBridge Energy Midstream Opportunity Fund Inc.

See Notes to Financial Statements.

Statement of assets and liabilities (unaudited)

May 31, 2021

See Notes to Financial Statements.

Statement of operations (unaudited)

For the Six Months Ended May 31, 2021

See Notes to Financial Statements.

Statements of changes in net assets

See Notes to Financial Statements.

Statement of cash flows (unaudited)

For the Six Months Ended May 31, 2021

See Notes to Financial Statements.

Financial highlights

See Notes to Financial Statements.

See Notes to Financial Statements.

Financial highlights (cont’d)

See Notes to Financial Statements.

Notes to financial statements (unaudited)

1. Organization and significant accounting policies

ClearBridge Energy Midstream Opportunity Fund Inc. (the “Fund”) was incorporated in Maryland on April 5, 2011 and is registered as a non-diversified, closed-end management investment company under the Investment Company Act of 1940, as amended (the “1940 Act”). The Board of Directors authorized 100 million shares of $0.001 par value common stock. The Fund’s investment objective is to provide long-term investors a high level of total return with an emphasis on cash distributions. There can be no assurance that the Fund will achieve its investment objective.

The Fund seeks to achieve its objective by investing primarily in energy midstream entities. Under normal market conditions, the Fund invests at least 80% of its Managed Assets in energy midstream entities including entities structured as both partnerships and corporations (the 80% policy). For purposes of the 80% policy, the Fund considers investments in midstream entities as those entities that provide midstream services including the gathering, transporting, processing, fractionation, storing, refining, and distribution of oil, natural gas liquids and natural gas. The Fund considers an entity to be within the Energy sector if it derives at least 50% of its revenues from the business of exploring, developing, producing, gathering, transporting, processing, fractionating, storing, refining, distributing, mining or marketing natural gas, natural gas liquids (including propane), crude oil, refined petroleum products or coal. “Managed Assets” means net assets plus the amount of borrowings and assets attributable to any preferred stock of the Fund that may be outstanding.

The following are significant accounting policies consistently followed by the Fund and are in conformity with U.S. generally accepted accounting principles (“GAAP”). Estimates and assumptions are required to be made regarding assets, liabilities and changes in net assets resulting from operations when financial statements are prepared. Changes in the economic environment, financial markets and any other parameters used in determining these estimates could cause actual results to differ. Subsequent events have been evaluated through the date the financial statements were issued.

(a) Investment valuation. Equity securities for which market quotations are available are valued at the last reported sales price or official closing price on the primary market or exchange on which they trade. The valuations for fixed income securities (which may include, but are not limited to, corporate, government, municipal, mortgage-backed, collateralized mortgage obligations and asset-backed securities) and certain derivative instruments are typically the prices supplied by independent third party pricing services, which may use market prices or broker/dealer quotations or a variety of valuation techniques and methodologies. The independent third party pricing services typically use inputs that are observable such as issuer details, interest rates, yield curves, prepayment speeds, credit risks/spreads, default rates and quoted prices for similar securities. Investments in open-end funds are valued at the closing net asset value per share of each fund on the day of valuation. When the Fund holds securities or other assets that are

Notes to financial statements (unaudited) (cont’d)

denominated in a foreign currency, the Fund will normally use the currency exchange rates as of 4:00 p.m. (Eastern Time). If independent third party pricing services are unable to supply prices for a portfolio investment, or if the prices supplied are deemed by the manager to be unreliable, the market price may be determined by the manager using quotations from one or more broker/dealers or at the transaction price if the security has recently been purchased and no value has yet been obtained from a pricing service or pricing broker. When reliable prices are not readily available, such as when the value of a security has been significantly affected by events after the close of the exchange or market on which the security is principally traded, but before the Fund calculates its net asset value, the Fund values these securities as determined in accordance with procedures approved by the Fund’s Board of Directors.

The Board of Directors is responsible for the valuation process and has delegated the supervision of the daily valuation process to the Global Fund Valuation Committee (formerly known as Legg Mason North Atlantic Fund Valuation Committee prior to March 1, 2021) (the “Valuation Committee”). The Valuation Committee, pursuant to the policies adopted by the Board of Directors, is responsible for making fair value determinations, evaluating the effectiveness of the Fund’s pricing policies, and reporting to the Board of Directors. When determining the reliability of third party pricing information for investments owned by the Fund, the Valuation Committee, among other things, conducts due diligence reviews of pricing vendors, monitors the daily change in prices and reviews transactions among market participants.

The Valuation Committee will consider pricing methodologies it deems relevant and appropriate when making fair value determinations. Examples of possible methodologies include, but are not limited to, multiple of earnings; discount from market of a similar freely traded security; discounted cash-flow analysis; book value or a multiple thereof; risk premium/yield analysis; yield to maturity; and/or fundamental investment analysis. The Valuation Committee will also consider factors it deems relevant and appropriate in light of the facts and circumstances. Examples of possible factors include, but are not limited to, the type of security; the issuer’s financial statements; the purchase price of the security; the discount from market value of unrestricted securities of the same class at the time of purchase; analysts’ research and observations from financial institutions; information regarding any transactions or offers with respect to the security; the existence of merger proposals or tender offers affecting the security; the price and extent of public trading in similar securities of the issuer or comparable companies; and the existence of a shelf registration for restricted securities.

For each portfolio security that has been fair valued pursuant to the policies adopted by the Board of Directors, the fair value price is compared against the last available and next

available market quotations. The Valuation Committee reviews the results of such back testing monthly and fair valuation occurrences are reported to the Board of Directors quarterly.

The Fund uses valuation techniques to measure fair value that are consistent with the market approach and/or income approach, depending on the type of security and the particular circumstance. The market approach uses prices and other relevant information generated by market transactions involving identical or comparable securities. The income approach uses valuation techniques to discount estimated future cash flows to present value.

GAAP establishes a disclosure hierarchy that categorizes the inputs to valuation techniques used to value assets and liabilities at measurement date. These inputs are summarized in the three broad levels listed below:

The inputs or methodologies used to value securities are not necessarily an indication of the risk associated with investing in those securities.

The following is a summary of the inputs used in valuing the Fund’s assets carried at fair value:

(b) Net asset value. The Fund determines the net asset value of its common stock on each day the NYSE is open for business, as of the close of the customary trading session

Notes to financial statements (unaudited) (cont’d)

(normally 4:00 p.m. Eastern Time), or any earlier closing time that day. The Fund determines the net asset value per share of common stock by dividing the value of the Fund’s securities, cash and other assets (including interest accrued but not collected) less all its liabilities (including accrued expenses, borrowings, interest payables and the aggregate liquidation value (i.e., $100,000 per outstanding share) of the Mandatory Redeemable Preferred Stock (“MRPS”)), net of income taxes, by the total number of shares of common stock outstanding.

(c) Master limited partnerships. Entities commonly referred to as “MLPs” are generally organized under state law as limited partnerships or limited liability companies. The Fund intends to primarily invest in MLPs receiving partnership taxation treatment under the Internal Revenue Code of 1986, as amended (the “Code”), and whose interests or “units” are traded on securities exchanges like shares of corporate stock. To be treated as a partnership for U.S. federal income tax purposes, an MLP whose units are traded on a securities exchange must receive at least 90% of its income from qualifying sources such as interest, dividends, real estate rents, gain from the sale or disposition of real property, income and gain from mineral or natural resources activities, income and gain from the transportation or storage of certain fuels, and, in certain circumstances, income and gain from commodities or futures, forwards and options with respect to commodities. Mineral or natural resources activities include exploration, development, production, processing, mining, refining, marketing and transportation (including pipelines) of oil and gas, minerals, geothermal energy, fertilizer, timber or industrial source carbon dioxide. An MLP consists of a general partner and limited partners (or in the case of MLPs organized as limited liability companies, a managing member and members). The general partner or managing member typically controls the operations and management of the MLP and has an ownership stake in the partnership. The limited partners or members, through their ownership of limited partner or member interests, provide capital to the entity, are intended to have no role in the operation and management of the entity and receive cash distributions. The MLPs themselves generally do not pay U.S. federal income taxes. Thus, unlike investors in corporate securities, direct MLP investors are generally not subject to double taxation (i.e., corporate level tax and tax on corporate dividends). Currently, most MLPs operate in the energy and/or natural resources sector.

(d) Foreign investment risks. The Fund’s investments in foreign securities may involve risks not present in domestic investments. Since securities may be denominated in foreign currencies, may require settlement in foreign currencies or pay interest or dividends in foreign currencies, changes in the relationship of these foreign currencies to the U.S. dollar can significantly affect the value of the investments and earnings of the Fund. Foreign investments may also subject the Fund to foreign government exchange restrictions, expropriation, taxation or other political, social or economic developments, all of which affect the market and/or credit risk of the investments.

(e) Concentration risk. Concentration in the energy sector may present more risks than if the Fund were broadly diversified over numerous sectors of the economy. A downturn in the energy sector of the economy could have a larger impact on the Fund than on an investment company that does not concentrate in the sector. At times, the performance of securities of companies in the sector may lag the performance of other sectors or the broader market as a whole.

(f) Security transactions and investment income. Security transactions are accounted for on a trade date basis. Interest income (including interest income from payment-in-kind securities), adjusted for amortization of premium and accretion of discount, is recorded on the accrual basis. Dividend income is recorded on the ex-dividend date for dividends received in cash and/or securities. Foreign dividend income is recorded on the ex-dividend date or as soon as practicable after the Fund determines the existence of a dividend declaration after exercising reasonable due diligence. The cost of investments sold is determined by use of the specific identification method. To the extent any issuer defaults or a credit event occurs that impacts the issuer, the Fund may halt any additional interest income accruals and consider the realizability of interest accrued up to the date of default or credit event.

(g) Return of capital estimates. Distributions received from the Fund’s investments in MLPs generally are comprised of income and return of capital. The Fund records investment income and return of capital based on estimates made at the time such distributions are received. Such estimates are based on historical information available from each MLP and other industry sources. These estimates may subsequently be revised based on information received from the MLPs after their tax reporting periods are concluded.

For the six months ended May 31, 2021, the Fund estimated that approximately 87% of the MLP distributions received would be treated as a return of capital. The Fund recorded as return of capital the amount of $13,763,190 of dividends and distributions received from its investments.

Additionally, the Fund updated the return of capital estimates from the year ended November 30, 2020 based on actual amounts subsequently reported to the Fund. This resulted in an increase of $497,915 in dividends and distributions received from investments.

(h) Partnership accounting policy. The Fund records its pro rata share of the income (loss) and capital gains (losses), to the extent of distributions it has received, allocated from the underlying partnerships and accordingly adjusts the cost basis of the underlying partnerships for return of capital. These amounts are included in the Fund’s Statement of Operations.

(i) Distributions to shareholders. Distributions to common shareholders are declared and paid on a quarterly basis and are recorded on the ex-dividend date. The estimated

Notes to financial statements (unaudited) (cont’d)

characterization of the distributions paid to common shareholders will be either a dividend (ordinary income), distribution (return of capital) or combination of both. This estimate is based on the Fund’s operating results during the period. The Fund anticipates that 100% of its current period distribution will be comprised of return of capital. The actual tax characterization of the common stock distributions made during the current year will not be determined until after the end of the fiscal year when the Fund can determine it’s earnings and profits and, therefore, may differ from the preliminary estimates.

Distributions to holders of MRPS are accrued on a daily basis as described in Note 7 and are treated as an operating expense as required by GAAP. For tax purposes, the payments made to the holders of the Fund’s MRPS are treated as a dividend (ordinary income) or distribution (return of capital) similar to the treatment of distributions made to common shareholders as described above. The Fund anticipates that 100% of its current period distribution to the MRPS shareholders will be treated as return of capital. The actual tax characterization of the MRPS distributions made during the current year will not be determined until after the end of the fiscal year when the Fund can determine its earnings and profits and, therefore, may differ from the preliminary estimates.

(j) Compensating balance arrangements. The Fund has an arrangement with its custodian bank whereby a portion of the custodian’s fees is paid indirectly by credits earned on the Fund’s cash on deposit with the bank.

(k) Federal and other taxes. The Fund, as a corporation, is obligated to pay federal and state income tax on its taxable income. The Fund invests its assets primarily in MLPs, which generally are treated as partnerships for federal income tax purposes. As a limited partner in the MLPs, the Fund includes its allocable share of the MLP’s taxable income in computing its own taxable income. The Fund, and entities in which the Fund invests, may be subject to audit by the Internal Revenue Service or other applicable tax authorities. The Fund’s taxable income or tax liability for prior taxable years could be adjusted if there is an audit of the Fund, or of any entity that is treated as a partnership for tax purposes in which the Fund holds an equity interest. The Fund may be required to pay tax, as well as interest and penalties, in connection with such an adjustment.

Deferred income taxes reflect (i) taxes on unrealized gains (losses), which are attributable to the temporary difference between fair market value and book basis, (ii) the net tax effects of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and the amounts used for income tax purposes and, as applicable, (iii) the net tax benefit of accumulated net operating losses, capital losses and tax credit carryforwards. To the extent the Fund has a deferred tax asset, consideration is given as to whether or not a valuation allowance is required. The need to establish a valuation allowance for deferred tax assets is assessed periodically by management of the Fund based on Financial Accounting Standards Board (“FASB”), Accounting Standards Codification Topic 740, Income Taxes (“ASC 740”) that it is more likely than not that some

portion or all of the deferred tax asset will not be realized. In the assessment for a valuation allowance, consideration is given to all positive and negative evidence related to the realization of the deferred tax asset. This assessment considers, among other matters, the nature, frequency and severity of current and cumulative losses, forecasts of future profitability (which are highly dependent on future allocations of taxable income and future cash distributions from the Fund’s MLP holdings), the duration of statutory carryforward periods and the associated risk that net operating losses, capital losses and tax credit carryforwards may expire unused.

For all open tax years and for all major jurisdictions, management of the Fund has concluded that there are no significant uncertain tax positions that would require recognition in the financial statements. Furthermore, management of the Fund is also not aware of any tax positions for which it is reasonably possible that the total amounts of unrecognized tax benefits will significantly change in the next twelve months.

The Fund may rely to some extent on information provided by the MLPs, which may not necessarily be timely, to estimate taxable income and gains allocable from the MLP units held in the portfolio and to estimate the associated deferred tax liability. Such estimates are made in good faith. From time to time, as new information becomes available, the Fund modifies its estimates or assumptions regarding the current and deferred tax liabilities.

The Fund’s policy is to classify interest and penalties associated with underpayment of federal and state income taxes, if any, as income tax expense on its Statement of Operations. The 2016 through 2020 tax years remain open and subject to examination by tax jurisdictions.

(l) Reclassification. GAAP requires that certain components of net assets be reclassified to reflect permanent differences between financial and tax reporting. These reclassifications have no effect on net assets or net asset value per share. During the six months ended May 31, 2021, the Fund had no reclassification.

2. Investment management agreement and other transactions with affiliates

Legg Mason Partners Fund Advisor, LLC (“LMPFA”) is the Fund’s investment manager and ClearBridge Investments, LLC (“ClearBridge”) is the Fund’s subadviser. LMPFA and ClearBridge are indirect, wholly-owned subsidiaries of Franklin Resources, Inc. (“Franklin Resources”).

Under the investment management agreement, the Fund pays LMPFA an annual fee, paid monthly, in an amount equal to 1.00% of the Fund’s average daily Managed Assets.

LMPFA provides administrative and certain oversight services to the Fund. LMPFA delegates to the subadviser the day-to-day portfolio management of the Fund. For its services, LMPFA pays ClearBridge a fee monthly, at an annual rate equal to 70% of the net management fee it receives from the Fund.

Notes to financial statements (unaudited) (cont’d)

During periods in which the Fund utilizes financial leverage, the fees paid to LMPFA will be higher than if the Fund did not utilize leverage because the fees are calculated as a percentage of the Fund’s assets, including those investments purchased with leverage.

Effective March 1, 2021, LMPFA implemented a voluntary investment management fee waiver of 0.05% that will continue until February 28, 2022.

During the six months ended May 31, 2021, fees waived and/or expenses reimbursed amounted to $57,699.

All officers and one Director of the Fund are employees of Franklin Resources or its affiliates and do not receive compensation from the Fund.

3. Investments

During the six months ended May 31, 2021, the aggregate cost of purchases and proceeds from sales of investments (excluding short-term investments) were as follows:

4. Derivative instruments and hedging activities

During the six months ended May 31, 2021, the Fund did not invest in derivative instruments.

5. Loan

The Fund has a revolving credit agreement with The Bank of Nova Scotia (“Credit Agreement”), which allows the Fund to borrow up to an aggregate amount of $75,000,000 and renews daily for a 179-day term, unless notice to the contrary is given to the Fund. Effective January 7, 2021, the Credit Agreement is subject to a scheduled commitment termination date of January 6, 2022, unless extended. The Fund pays a commitment fee on the unutilized portion of the loan commitment amount at an annual rate of 0.25%, except that the commitment fee is 0.15% in the event that the aggregate outstanding principal balance of the loan is equal to or greater than 75% of $75,000,000. The interest on the loan is calculated at a variable rate based on LIBOR plus any applicable margin. Securities held by the Fund are subject to a lien, granted to The Bank of Nova Scotia, to the extent of the borrowing outstanding and any additional expenses. The Fund’s Credit Agreement contains customary covenants that, among other things, may limit the Fund’s ability to pay distributions in certain circumstances, incur additional debt, change its fundamental investment policies and engage in certain transactions, including mergers and consolidations and require asset coverage ratios in addition to those required by the 1940 Act. In addition, the Credit Agreement may be subject to early termination under certain conditions and may contain other provisions that could limit the Fund’s ability to utilize borrowing under the agreement. At May 31, 2021, the Fund had $57,000,000 of borrowings outstanding per this credit agreement. Interest expense related to this loan for the six

months ended May 31, 2021 was $191,116. For the six months ended May 31, 2021, the Fund incurred commitment fees of $54,263. For the year ended May 31, 2021, based on the number of days during the reporting period that the Fund had a loan balance outstanding, the average daily loan balance was $32,065,934 and the weighted average interest rate was 1.20%.

6. Senior secured notes

At May 31, 2021, the Fund had $45,103,579 aggregate principal amount of fixed-rate senior secured notes (“Senior Notes”) outstanding. Interest expense related to the Senior Notes for the six months ended May 31, 2021 was $944,261. Costs incurred by the Fund in connection with the Senior Notes are recorded as a deferred charge and are amortized over the life of the notes. Securities held by the Fund are subject to a lien, granted to the Senior Notes holders, to the extent of the borrowings outstanding and any additional expenses. The Senior Notes holders and the lender have equal access to the lien (See Note 5).

On February 7, 2020, Series A Senior Notes in the amount of $27,420,382 matured. On October 15, 2020 Series F Senior Notes in the amount of $8,176,039 matured.

The table below summarizes the key terms of each series of Senior Notes at May 31, 2021.

The Senior Notes are not listed on any exchange or automated quotation system. The estimated fair value of the Senior Notes was calculated, for disclosure purposes, based on estimated market yields and credit spreads for comparable instruments with similar maturity, terms and structure. The Senior Notes are categorized as Level 3 within the fair value hierarchy.

7. Mandatory redeemable preferred stock

At May 31, 2021, the Fund had 431 shares of fixed rate MRPS outstanding with an aggregate liquidation value of $43,100,000. Offering costs incurred by the Fund in connection with the MRPS issuance are being amortized to expense over the respective life of each series of MRPS.

Notes to financial statements (unaudited) (cont’d)

The table below summarizes the key terms of each series of the MRPS at May 31, 2021.

The MRPS are not listed on any exchange or automated quotation system. The estimated fair value of the MRPS was calculated, for disclosure purposes, based on estimated market yields and credit spreads for comparable instruments with similar maturity, terms and structure. The MRPS are categorized as Level 3 within the fair value hierarchy.

Holders of MRPS are entitled to receive quarterly cumulative cash dividends payable on the first business day following each quarterly dividend date (February 15, May 15, August 15 and November 15). In the event of a rating downgrade of any series of the MRPS below “A” by Fitch Ratings Inc. (“Fitch”) or other nationally recognized statistical ratings organization then providing a rating, the applicable dividend rate will increase, according to a predetermined schedule, by 0.5% to 4.0%. In March 2020, Fitch revised its ratings assigned to the MRPS from “AA” to “BBB” and, consequently, holders of MRPS were entitled to receive enhanced dividends by 2.0%. Effective January 22, 2021, after Fitch withdrew its ratings and Kroll Bond Rating Agency (“KBRA”) assigned the rating of “A” to each series of the Fund’s MRPS, the holders receive dividends payable at the rates shown in the table above.

The MRPS rank senior to the Fund’s outstanding common stock and on parity with any other preferred stock. The Fund may, at its option, redeem the MRPS, in whole or in part, at the liquidation preference amount plus all accumulated but unpaid dividends plus the make whole amount equal to the discounted value of the remaining scheduled payments. If the Fund fails to maintain a total leverage (debt and preferred stock) asset coverage ratio of at least 225% or is in default of specified rating agency requirements, the MRPS are subject to mandatory redemption under certain provisions.

The Fund may not declare dividends or make other distributions on shares of its common stock unless the Fund has declared and paid full cumulative dividends on the MRPS, due on or prior to the date of the common stock dividend or distribution, and meets the MRPS asset coverage and rating agency requirements.

The holders of the MRPS have one vote per share and vote together with the holders of common stock of the Fund as a single class, except on matters affecting only the holders of

MRPS or the holders of common stock. Pursuant to the 1940 Act, holders of the MRPS have the right to elect two Directors of the Fund, voting separately as a class.

8. Stock repurchase program

On November 16, 2015, the Fund announced that the Fund’s Board of Directors (the “Board”) had authorized the Fund to repurchase in the open market up to approximately 10% of the Fund’s outstanding common stock when the Fund’s shares are trading at a discount to net asset value. The Board has directed management of the Fund to repurchase shares of common stock at such times and in such amounts as management reasonably believes may enhance stockholder value. The Fund is under no obligation to purchase shares at any specific discount levels or in any specific amounts.

During the six months ended May 31, 2021, the Fund repurchased and retired 3.91% of its common shares outstanding under the repurchase plan. The weighted average discount per share on these repurchases was 21.19% for the six months ended May 31, 2021. Shares repurchased and the corresponding dollar amount are included in the Statements of Changes in Net Assets. The anti-dilutive impact of these share repurchases is included in the Financial Highlights.

Since the commencement of the stock repurchase program through May 31, 2021, the Fund repurchased 1,139,496 shares or 7.22% of its common shares outstanding for a total amount of $14,447,022.

9. Reverse stock split

On July 14, 2020, the Fund announced that the Fund’s Board had approved a 1-for-5 reverse stock split, which was completed prior to the open of trading on the New York Stock Exchange on July 28, 2020. As a result of the reverse stock split, every five outstanding shares of common stock of the Fund were automatically converted into one share of common stock. The reverse stock split decreased the number of the Fund’s shares of common stock outstanding and increased the net asset value per share by a proportional amount. Neither the Fund’s portfolio holdings nor the total value of stockholders’ investments in the Fund were affected as a result of the reverse stock split. The details of the reverse stock split are as follows:

Notes to financial statements (unaudited) (cont’d)

10. Restricted securities

The following Fund investment is restricted as to resale and, in the absence of a readily ascertainable market value, is valued in good faith in accordance with procedures approved by the Board of Directors.

11. Income taxes

On March 27, 2020, the Coronavirus Aid, Relief, and Economic Security Act (“CARES Act”) was enacted in response to the COVID-19 pandemic. The CARES Act contains several corporate income tax provisions, including but not limited to, (1) providing a 5-year carryback of net operating loss (“NOL”) tax carryforwards generated in tax years beginning after December 31, 2017 and before January 1, 2021; (2) temporarily removing the 80% taxable income limitation on NOL utilization for tax years beginning before January 1, 2021; (3) temporarily increasing the allowable interest expense deductions under Sec. 163(j) of the Code; and (4) accelerating the refundability of corporate alternative minimum tax credits. The Fund continues to evaluate the potential impact for the year ended November 30, 2021.

The Fund’s federal and state income tax provision consist of the following:

Total income taxes have been computed by applying the U.S. federal statutory income tax rate of 21% plus a blended net state income tax rate of 1.7%. The Fund applied this rate to net investment income (loss) and realized and unrealized gains (losses) on investments before income taxes in computing its total income tax expense (benefit).

The provision for income taxes differs from the amount derived from applying the statutory income tax rate to net investment income (loss) and realized and unrealized gains (losses) before income taxes as follows:

Components of the Fund’s net deferred tax asset (liability) as of May 31, 2021 are as follows:

At May 31, 2021, the Fund had federal and state net operating loss carryforwards of $157,576,272 and $70,574,076 (net of state apportionment), respectively (deferred tax asset of $37,008,773). Several states compute net operating losses before apportionment, therefore the value of the state net operating loss carryforward disclosed may fluctuate for changes in apportionment factors. Realization of the deferred tax asset related to the net operating loss carryforwards is dependent, in part, on generating sufficient taxable income in each respective jurisdiction prior to expiration of the loss carryforwards. If not utilized, the federal net operating loss carryforward expires in tax years 2033 and 2036, and the state net operating loss carryforwards expire in tax years between 2020 and 2040. The federal net operating loss carryforward generated in the current year does not have an expiration.

Additionally, at May 31, 2021, the Fund had a federal and state capital loss carryforward of $388,217,837 (deferred tax asset of $88,125,449), which may be carried forward for 5 years. If not utilized, this capital loss carryforward expires in tax years 2020, 2023, 2024 and 2025. For corporations, capital losses can only be used to offset capital gains and cannot be used to offset ordinary income. Therefore, the use of this capital loss carryforward is dependent upon the Fund generating sufficient net capital gains prior to the expiration of the loss carryforward.

As a result of the November 16, 2018 acquisition of ClearBridge American Energy MLP Fund, Inc., the Fund’s pre-acquisition loss carryovers are now subject to an annual limitation of approximately $8.0 million under Section 382 of the Code. Additionally, under Section 384 of the Code, the Fund is limited in its ability to use the acquired fund’s loss carryovers to offset the recognition of its “built-in gains” in assets that existed at the time of the acquisition for a period of five-years.

The amount of net operating loss and capital loss carryforwards differed from the amounts disclosed in the prior year financial statements due to differences between the estimated and actual amounts of taxable income received from the MLPs for the prior year.

Notes to financial statements (unaudited) (cont’d)

Significant declines in the fair market value of its portfolio of investments, in conjunction with cumulative net operating losses and capital losses incurred and expected to be incurred, have resulted in the Fund having a net deferred tax asset as of May 31, 2021. Based on the assessment, as described in Note 1(k), and considering the limitations imposed under Sections 382 and 384 as discussed above, management of the Fund has determined that it is not more likely than not that it will be able to generate significant future taxable income of the appropriate character in order to realize its deferred tax assets. Accordingly, management of the Fund has determined that a full valuation allowance on its net deferred tax asset is appropriate at this time.

At May 31, 2021, the cost basis of investments for Federal income tax purposes was $396,898,873. At May 31, 2021, gross unrealized appreciation and depreciation of investments for Federal income tax purposes were as follows:

12. Recent accounting pronouncement

In March 2020, the Financial Accounting Standards Board issued Accounting Standards Update No. 2020-04, Reference Rate Reform (Topic 848) – Facilitation of the Effects of Reference Rate Reform on Financial Reporting (the “ASU”). The amendments in the ASU provide optional temporary financial reporting relief from the effect of certain types of contract modifications due to the planned discontinuation of the London Interbank Offered Rate and other interbank-offered based reference rates as of the end of 2021. The ASU is effective for certain reference rate-related contract modifications that occur during the period March 12, 2020 through December 31, 2022. Management has reviewed the requirements and believes the adoption of this ASU will not have a material impact on the financial statements.

13. Other matters

The outbreak of the respiratory illness COVID-19 (commonly referred to as “coronavirus”) has continued to rapidly spread around the world, causing considerable uncertainty for the global economy and financial markets. The ultimate economic fallout from the pandemic, and the long-term impact on economies, markets, industries and individual issuers, are not known. The COVID-19 pandemic could adversely affect the value and liquidity of the Fund’s investments and negatively impact the Fund’s performance. In addition, the outbreak of COVID-19, and measures taken to mitigate its effects, could result in disruptions to the services provided to the Fund by its service providers.

*  *  *

The London Interbank Offered Rate, or “LIBOR,” the offered rate for short-term Eurodollar deposits between major international banks, is used extensively in the United States and globally as a reference rate in various financing and commercial transactions. On March 5, 2021, the ICE Benchmark Administration, the administrator of LIBOR, stated that it will cease the publication of (i) the overnight and one-, three-, six- and twelve-month USD LIBOR settings immediately following the LIBOR publication on Friday, June 30, 2023 and (ii) all other LIBOR settings, including the one-week and two-month USD LIBOR settings, immediately following the LIBOR publication on Friday, December 31, 2021. There remains uncertainty regarding the nature of any replacement rate and the impact of the transition from LIBOR on the financial markets generally, transactions that use LIBOR as a reference rate and financial institutions that engage in such transactions, including issuers of securities in which the Fund invests. As such, the potential effect of a transition away from LIBOR on the Fund or the Fund’s investments cannot yet be determined.

Additional shareholder information (unaudited)

Results of annual meeting of shareholders

The Annual Meeting of Shareholders of ClearBridge Energy Midstream Opportunity Fund Inc. was held on June 4, 2021 for the purpose of considering and voting upon the proposals presented at the Meeting. The following table provides information concerning the matters voted upon at the Meeting:

Election of directors

At May 31, 2021, in addition to Carol L. Colman, Daniel P. Cronin and Paolo M. Cucchi, the other Directors of the Fund were as follows:

Robert D. Agdern

William R. Hutchinson

Eileen A. Kamerick

Nisha Kumar

Jane Trust

Ratification of Selection of Independent Registered Public Accountants

To ratify the selection of PricewaterhouseCoopers LLP (“PwC”) as independent registered public accountants of the Fund for the fiscal year ended November 30, 2021.

Dividend reinvestment plan (unaudited)

Unless you elect to receive distributions in cash (i.e., opt-out), all dividends, including any capital gain dividends and return of capital distributions, on your Common Stock will be automatically reinvested by Computershare Trust Company, N.A., as agent for the stockholders (the “Plan Agent”), in additional shares of Common Stock under the Fund’s Dividend Reinvestment Plan (the “Plan”). You may elect not to participate in the Plan by contacting the Plan Agent. If you do not participate, you will receive all cash distributions paid by check mailed directly to you by Computershare Trust Company, N.A., as dividend paying agent.

If you participate in the Plan, the number of shares of Common Stock you will receive will be determined as follows:

(1) If the market price of the Common Stock (plus $0.03 per share commission) on the payment date (or, if the payment date is not a NYSE trading day, the immediately preceding trading day) is equal to or exceeds the net asset value per share of the Common Stock at the close of trading on the NYSE on the payment date, the Fund will issue new Common Stock at a price equal to the greater of (a) the net asset value per share at the close of trading on the NYSE on the payment date or (b) 95% of the market price per share of the Common Stock on the payment date.

(2) If the net asset value per share of the Common Stock exceeds the market price of the Common Stock (plus $0.03 per share commission) at the close of trading on the NYSE on the payment date, the Plan Agent will receive the dividend or distribution in cash and will buy Common Stock in the open market, on the NYSE or elsewhere, for your account as soon as practicable commencing on the trading day following the payment date and terminating no later than the earlier of (a) 30 days after the dividend or distribution payment date, or (b) the payment date for the next succeeding dividend or distribution to be made to the stockholders; except when necessary to comply with applicable provisions of the federal securities laws. If during this period: (i) the market price (plus $0.03 per share commission) rises so that it equals or exceeds the net asset value per share of the Common Stock at the close of trading on the NYSE on the payment date before the Plan Agent has completed the open market purchases or (ii) if the Plan Agent is unable to invest the full amount eligible to be reinvested in open market purchases, the Plan Agent will cease purchasing Common Stock in the open market and the Fund shall issue the remaining Common Stock at a price per share equal to the greater of (a) the net asset value per share at the close of trading on the NYSE on the day prior to the issuance of shares for reinvestment or (b) 95% of the then current market price per share.

Common Stock in your account will be held by the Plan Agent in non-certificated form. Any proxy you receive will include all shares of Common Stock you have received under the Plan. You may withdraw from the Plan (i.e., opt-out) by notifying the Plan Agent in writing at 462 South 4th Street, Suite 1600, Louisville, KY 40202 or by calling the Plan Agent at 1-888-888-0151. Such withdrawal will be effective immediately if notice is received by the Plan Agent not less than ten business days prior to any dividend or distribution record date;

Dividend reinvestment plan (unaudited) (cont’d)

otherwise such withdrawal will be effective as soon as practicable after the Plan Agent’s investment of the most recently declared dividend or distribution on the Common Stock.

Plan participants who sell their shares will be charged a service charge (currently $5.00 per transaction) and the Plan Agent is authorized to deduct brokerage charges actually incurred from the proceeds (currently $0.05 per share commission). There is no service charge for reinvestment of your dividends or distributions in Common Stock. However, all participants will pay a pro rata share of brokerage commissions incurred by the Plan Agent when it makes open market purchases. Because all dividends and distributions will be automatically reinvested in additional shares of Common Stock, this allows you to add to your investment through dollar cost averaging, which may lower the average cost of your Common Stock over time. Dollar cost averaging is a technique for lowering the average cost per share over time if the Fund’s net asset value declines. While dollar cost averaging has definite advantages, it cannot assure profit or protect against loss in declining markets.

Automatically reinvesting dividends and distributions does not mean that you do not have to pay income taxes due upon receiving dividends and distributions. Investors will be subject to income tax on amounts reinvested under the Plan.

The Fund reserves the right to amend or terminate the Plan if, in the judgment of the Board of Directors, the change is warranted. The Plan may be terminated, amended or supplemented by the Fund upon notice in writing mailed to stockholders at least 30 days prior to the record date for the payment of any dividend or distribution by the Fund for which the termination or amendment is to be effective. Upon any termination, you will be sent cash for any fractional share of Common Stock in your account. You may elect to notify the Plan Agent in advance of such termination to have the Plan Agent sell part or all of your Common Stock on your behalf. Additional information about the Plan and your account may be obtained from the Plan Agent at 462 South 4th Street, Suite 1600, Louisville, KY 40202 or by calling the Plan Agent at 1-888-888-0151.

ClearBridge

Energy Midstream Opportunity Fund Inc.

Directors

Robert D. Agdern

Carol L. Colman

Daniel P. Cronin

Paolo M. Cucchi

William R. Hutchinson

Eileen A. Kamerick

Nisha Kumar

Jane Trust

Chairman

Officers

Jane Trust

President and Chief Executive Officer

Christopher Berarducci

Treasurer and Principal Financial Officer

Fred Jensen

Chief Compliance Officer

Jenna Bailey

Identity Theft Prevention Officer

George P. Hoyt

Secretary and Chief Legal Officer

Thomas C. Mandia

Assistant Secretary

Jeanne M. Kelly

Senior Vice President

ClearBridge Energy Midstream Opportunity Fund Inc.

620 Eighth Avenue

47th Floor

New York, NY 10018

Investment manager

Legg Mason Partners Fund Advisor, LLC

Subadviser

ClearBridge Investments, LLC

Custodian

The Bank of New York Mellon

Transfer agent

Computershare Inc.

462 South 4th Street, Suite 1600

Louisville, KY 40202

Independent registered public accounting firm

PricewaterhouseCoopers LLP

Baltimore, MD

Legal counsel

Simpson Thacher & Bartlett LLP

425 Lexington Avenue

New York, NY 10017

New York Stock Exchange Symbol

EMO

Legg Mason Funds Privacy and Security Notice

Your Privacy and the Security of Your Personal Information is Very Important to the Legg Mason Funds

This Privacy and Security Notice (the “Privacy Notice”) addresses the Legg Mason Funds’ privacy and data protection practices with respect to nonpublic personal information the Funds receive. The Legg Mason Funds include any funds sold by the Funds’ distributor, Legg Mason Investor Services, LLC, as well as Legg Mason-sponsored closed-end funds. The provisions of this Privacy Notice apply to your information both while you are a shareholder and after you are no longer invested with the Funds.

The Type of Nonpublic Personal Information the Funds Collect About You

The Funds collect and maintain nonpublic personal information about you in connection with your shareholder account. Such information may include, but is not limited to:

How the Funds Use Nonpublic Personal Information About You

The Funds do not sell or share your nonpublic personal information with third parties or with affiliates for their marketing purposes, or with other financial institutions or affiliates for joint marketing purposes, unless you have authorized the Funds to do so. The Funds do not disclose any nonpublic personal information about you except as may be required to perform transactions or services you have authorized or as permitted or required by law.

The Funds may disclose information about you to:

Legg Mason Funds Privacy and Security Notice (cont’d)

Except as otherwise permitted by applicable law, companies acting on the Funds’ behalf, including those outside the United States, are contractually obligated to keep nonpublic personal information the Funds provide to them confidential and to use the information the Funds share only to provide the services the Funds ask them to perform. The Funds may disclose nonpublic personal information about you when necessary to enforce their rights or protect against fraud, or as permitted or required by applicable law, such as in connection with a law enforcement or regulatory request, subpoena, or similar legal process. In the event of a corporate action or in the event a Fund service provider changes, the Funds may be required to disclose your nonpublic personal information to third parties. While it is the Funds’ practice to obtain protections for disclosed information in these types of transactions, the Funds cannot guarantee their privacy policy will remain unchanged.

Keeping You Informed of the Funds’ Privacy and Security Practices

The Funds will notify you annually of their privacy policy as required by federal law. While the Funds reserve the right to modify this policy at any time they will notify you promptly if this privacy policy changes.

The Funds’ Security Practices

The Funds maintain appropriate physical, electronic and procedural safeguards designed to guard your nonpublic personal information. The Funds’ internal data security policies restrict access to your nonpublic personal information to authorized employees, who may use your nonpublic personal information for Fund business purposes only.

Although the Funds strive to protect your nonpublic personal information, they cannot ensure or warrant the security of any information you provide or transmit to them, and you do so at your own risk. In the event of a breach of the confidentiality or security of your nonpublic personal information, the Funds will attempt to notify you as necessary, so you can take appropriate protective steps. If you have consented to the Funds using electronic communications or electronic delivery of statements, they may notify you under such circumstances using the most current email address you have on record with them.

In order for the Funds to provide effective service to you, keeping your account information accurate is very important. If you believe that your account information is incomplete, not accurate or not current, if you have questions about the Funds’ privacy practices, or our use of your nonpublic personal information, write the Funds using the contact information on your account statements, email the Funds by clicking on the Contact Us section of the Funds’ website at www.leggmason.com, or contact the Fund at 1-888-777-0102.

Revised April 2018

Legg Mason California Consumer Privacy Act Policy

Although much of the personal information we collect is “nonpublic personal information” subject to federal law, residents of California may, in certain circumstances, have additional rights under the California Consumer Privacy Act (“CCPA”). For example, if you are a broker,

Legg Mason Funds Privacy and Security Notice (cont’d)

dealer, agent, fiduciary, or representative acting by or on behalf of, or for, the account of any other person(s) or household, or a financial advisor, or if you have otherwise provided personal information to us separate from the relationship we have with personal investors, the provisions of this Privacy Policy apply to your personal information (as defined by the CCPA).

If you wish to exercise any of the rights you have in respect of your personal information, you should advise the Funds by contacting them as set forth below. The rights noted above are subject to our other legal and regulatory obligations and any exemptions under the CCPA. You may designate an authorized agent to make a rights request on your behalf, subject to the identification process described below. We do not discriminate based on requests for information related to our use of your personal information, and you have the right not to receive discriminatory treatment related to the exercise of your privacy rights.

We may request information from you in order to verify your identity or authority in making such a request. If you have appointed an authorized agent to make a request on your behalf, or you are an authorized agent making such a request (such as a power of attorney or other written permission), this process may include providing a password/passcode, a copy of government issued identification, affidavit or other applicable documentation, i.e. written permission. We may require you to verify your identity directly even when using an authorized agent, unless a power of attorney has been provided. We reserve the right to deny a request submitted by an agent if suitable and appropriate proof is not provided.

For the 12-month period prior to the date of this Privacy Policy, the Legg Mason Funds have not sold any of your personal information; nor do we have any plans to do so in the future.

Contact Information

Address: Data Privacy Officer, 100 International Dr., Baltimore, MD 21202

Email: DataProtectionOfficer@franklintempleton.com

Phone: 1-800-396-4748

Revised October 2020

ClearBridge Energy Midstream Opportunity Fund Inc.

ClearBridge Energy Midstream Opportunity Fund Inc.

620 Eighth Avenue

47^th Floor

New York, NY 10018

Notice is hereby given in accordance with Section 23(c) of the Investment Company Act of 1940, as amended, that from time to time the Fund may purchase, at market prices, shares of its stock.

The Fund files its complete schedule of portfolio holdings with the Securities and Exchange Commission (“SEC”) for the first and third quarters of each fiscal year as an exhibit to its reports on Form N-PORT. The Fund’s Forms N-PORT are available on the SEC’s website at www.sec.gov. To obtain information on Form N-PORT, shareholders can call the Fund at 1-888-777-0102.

Information on how the Fund voted proxies relating to portfolio securities during the prior 12-month period ended June 30th of each year and a description of the policies and procedures that the Fund uses to determine how to vote proxies related to portfolio transactions are available (1) without charge, upon request, by calling 1-888-777-0102, (2) at www.lmcef.com and (3) on the SEC’s website at www.sec.gov.

This report is transmitted to the shareholders of ClearBridge Energy Midstream Opportunity Fund Inc. for their information. This is not a prospectus, circular or representation intended for use in the purchase of shares of the Fund or any securities mentioned in this report.

Computershare Inc.

462 South 4th Street, Suite 1600

Louisville, KY 40202

CBAX014784 7/21 SR21-4188