EMO ClearBridge Energy Midstream Opportunity Fund Inc

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

(Rule 14a-101)

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

(Amendment No.    )

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Filed by a Party other than the Registrant  ☐

Check the appropriate box:

CLEARBRIDGE ENERGY MIDSTREAM OPPORTUNITY FUND INC.

(Name of Registrant as Specified in Its Charter)

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ClearBridge Investments Please Vote on the WHITE Proxy Card CLEARBRIDGE ENERGY MIDSTREAM OPPORTUNITY FUND INC. (EMO) Your Vote Is Important, No Matter How Many or How Few Shares You Own March 30, 2023 Dear Stockholder: The ClearBridge Energy Midstream Opportunity Fund Inc. (the “Fund” or “EMO”) Annual Meeting of Stockholders will be held on April 14, 2023 (the “Annual Meeting”). Please vote on the WHITE Proxy Card today to support the Board that is taking action to drive strong returns and increase distributions for you. The Board unanimously recommends you vote “FOR” the election of the Fund’s Board Nominee on the enclosed WHITE proxy card to ensure the Board can continue to build on its track record of advancing your interests. Under the Board’s leadership, the Fund has a strong track record of delivering competitive financial performance, which has allowed it to significantly increase its distributions to you, including growing distributions by 28.3% over the last five quarters. DIVIDEND INCREASES $0.39 $0.50 $0.51 $0.52 $0.53 2.28.22 5.31.22 8.31.22 11.30.22 2.28.23 FRANKLIN TEMPLETON

The Board is committed to advancing the Fund’s investment objective — delivering a high level of total return with an emphasis on cash distributions. The Board’s success in achieving this objective is evident in the strong outperformance the Fund has delivered over the last several years. HISTORY OF OUTPERFORMANCE Annual Returns Based on Market Price 2022 2021 74.80% 53.73% 40.16% 25.69% EMO Lipper Peer Average EMO Lipper Peer Average The Fund’s Board Has the Right Mix of Skills and Experience to Continue Overseeing EMO’s Strategy to Enhance Value for All Stockholders The Board is carefully constructed to ensure that we have the right mix of skills and diverse voices to achieve independent and well-rounded oversight of our strategy. The Board comprises seven highly qualified, experienced directors, six of whom are independent and the majority of whom are women, including the Board Chair. Executive / Managerial Public or Fund Company Board NYSE Qualified Audit to Committee be SEC / Global Consulting Business & Legal & Risk Leadership Position Financial Expert Expertise Oversight Robert D. Agdern Eileen A. Kamerick Daniel P. Cronin Paolo M. Cucchi Nisha Kumar Carol L. Colman, CFA Jane E. Trust, CFA

As a Common Stockholder, You Have the Opportunity to Protect the Value Of Your Investment by Voting “FOR” the Fund’s Highly Qualified Nominee, Robert D. Agdern Robert D. Agdern is an experienced business and legal professional with over 25 years of experience in the oil and gas industry and currently serves as the Fund’s Compliance Liaison. Mr. Agdern also held various leadership positions with Amoco Corporation, including Exploration and Production Company General Counsel and Executive Vice President — Natural Gas; Chemical Company General Counsel; and Associate General Counsel, Amoco Corporation. Mr. Agdern formerly served as Deputy General Counsel for BP PLC and as a Member of the Advisory Committee of the Dispute Resolution Research Center at the Kellogg Graduate School of Business, Northwestern University. Mr. Agdern has served on the Fund’s Board since 2015 and has extensive experience serving as a director for registered, closed-end investment companies. We urge you NOT to return any gold proxy card that you receive, as that vote will not count as a vote in support of the Fund’s Board. If you vote your shares more than once, only your latest-dated proxy card counts. Protect the Value of Your Investment. Vote on the Enclosed WHITE Proxy Card Today Whether or not you plan to attend the Annual Meeting, you have an opportunity to protect the value of your investment by voting on the WHITE Proxy Card “FOR” the Fund’s nominee.

ClearBridge Investments Your vote is important, no matter how many or how few shares you own. You can vote by internet, telephone or by signing and dating the WHITE Proxy Card or Voting Instruction Form and mailing it in the envelope provided. If you have any questions about how to vote your shares or need additional assistance, please contact: Georgeson LLC: 1 (800) 868-1391 Forward Looking Statement Past performance is no guarantee of future results. The information provided is not intended to be a forecast of future events, a guarantee of future results or investment advice. All investments are subject to risk including the possible loss of principal. All benchmark performance reflects no deduction for fees, expenses or taxes. Please note that an investor cannot invest directly in a benchmark. FRANKLIN TEMPLETON