exhibit992-sx4a

1 U P X Using a black ink pen, mark your votes with an X as shown in this example. Please do not write outside the designated areas. 03W5QD + + Please sign exactly as name(s) appears hereon. Joint owners should each sign. When signing as attorney, executor, administrator, corporate officer, trustee, guardian, or custodian, please give full title. Signature 1 — Please keep signature within the box. Signature 2 — Please keep signature within the box.Date (mm/dd/yyyy) — Please print date below. Authorized Signatures — This section must be completed for your vote to count. Please date and sign below.B q IF VOTING BY MAIL, SIGN, DETACH AND RETURN THE BOTTOM PORTION IN THE ENCLOSED ENVELOPE. q 2023 Special Meeting Proxy Card CONTROL NUMBER: Proposals — The Board of Directors recommends a vote FOR Proposals 1, 2 and 3.A 1. To approve the Agreement and Plan of Reorganization and accompanying Plan of Merger, dated as of August 24, 2023 (the “merger agreement”), by and between Burke & Herbert Financial Services Corp. (“Burke & Herbert”) and Summit Financial Group, Inc. (“Summit”), and the other transactions contemplated by the merger agreement, pursuant to which Summit will merge with and into Burke & Herbert as more fully described in the accompanying joint proxy statement/prospectus. For Against Abstain For Against Abstain 3. To adjourn the Summit special meeting, if necessary or appropriate, to solicit additional proxies if, immediately prior to such adjournment, there are not sufficient votes to approve the Summit merger proposal or to ensure that any supplement or amendment to the accompanying joint proxy statement/prospectus is timely provided to holders of Summit common stock. Note: Consummation of the merger and other transactions contemplated by the merger agreement is not conditioned on Proposal 3. IF THIS PROXY IS PROPERLY SIGNED AND IS NOT REVOKED, THIS PROXY WILL BE VOTED AS DIRECTED, BUT IF NO INSTRUCTIONS ARE SPECIFIED, THIS PROXY WILL BE VOTED FOR APPROVAL OF ALL PROPOSALS. IF ANY OTHER BUSINESS IS PROPERLY PRESENTED AT THE MEETING, OR ANY ADJOURNMENT OR POSTPONEMENT THEREOF, THIS PROXY WILL BE VOTED BY THOSE NAMED IN THIS PROXY IN THEIR BEST JUDGMENT. 2. To approve, on an advisory (non-binding) basis, the merger-related compensation payments that will or may be paid to the named executive officers of Summit in connection with the transactions contemplated by the merger agreement. For Against Abstain M M M M M M M M M 5 9 0 5 6 6 MR A SAMPLE (THIS AREA IS SET UP TO ACCOMMODATE 140 CHARACTERS) MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND MR A SAMPLE AND C 1234567890 J N T MMMMMMMMMMMM MMMMMMM 1234 5678 9012 345 0 0 0 0 0 1 MR A SAMPLE DESIGNATION (IF ANY) ADD 1 ADD 2 ADD 3 ADD 4 ADD 5 ADD 6 ENDORSEMENT_LINE______________ SACKPACK_____________ MMMMMMMMMMMMMMM C123456789 000000000.000000 ext 000000000.000000 ext 000000000.000000 ext 000000000.000000 ext 000000000.000000 ext 000000000.000000 ext Save paper, time and money! Sign up for electronic delivery at www.investorvote.com/SMMF Phone Call toll free 1-800-652-VOTE (8683) within the USA, US territories and Canada You may vote online or by phone instead of mailing this card. Your vote matters – here’s how to vote! Online Go to www.investorvote.com/SMMF or scan the QR code — login details are located in the shaded bar below. Votes submitted electronically must be received by 1:00 pm, Eastern Time, on December 6, 2023. Exhibit 99.2

Notice of 2023 Special Meeting of Shareholders Proxy Solicited by Board of Directors for Special Meeting — December 6, 2023 The undersigned shareholder(s) of Summit Financial Group, Inc. (“Summit”) hereby appoints Julie R. Markwood and Teresa D. Ely, or either of them, with the power of substitution, to represent and vote the shares of the undersigned, with all the powers which the undersigned would possess if personally present, at the Special Meeting of Shareholders of Summit Financial Group, Inc. to be held on December 6, 2023, or at any postponement or adjournment thereof. The undersigned acknowledges receipt of the Notice and Joint Proxy Statement/Prospectus dated October 16, 2023, and hereby revokes all proxies previously given by the undersigned for said meeting. Shares represented by this proxy will be voted as specified by the shareholder. If no such directions are indicated, the Proxies will have authority to vote FOR Proposals 1, 2 and 3. The Board of Directors recommends a vote “FOR” Proposals 1, 2 and 3. In their discretion, the Proxies are authorized to vote upon such other business as may properly come before the meeting. (Items to be voted appear on reverse side) SUMMIT FINANCIAL GROUP, INC. q IF VOTING BY MAIL, SIGN, DETACH AND RETURN THE BOTTOM PORTION IN THE ENCLOSED ENVELOPE. q Change of Address — Please print new address below. Comments — Please print your comments below. Non-Voting ItemsC + + IMPORTANT NOTICE REGARDING THE AVAILABILITY OF PROXY MATERIALS FOR THE SPECIAL MEETING OF SHAREHOLDERS TO BE HELD ON DECEMBER 6, 2023 2023 Special Meeting of Summit Financial Group, Inc. Shareholders will be held on December 6, 2023, 1:00 p.m. ET at Summit Financial Group, Inc. Headquarters 300 North Main Street, Moorefield, WV 26836

1 U P X Using a black ink pen, mark your votes with an X as shown in this example. Please do not write outside the designated areas. 03W5RD + + Please sign exactly as name(s) appears hereon. Joint owners should each sign. When signing as attorney, executor, administrator, corporate officer, trustee, guardian, or custodian, please give full title. Signature 1 — Please keep signature within the box. Signature 2 — Please keep signature within the box.Date (mm/dd/yyyy) — Please print date below. Authorized Signatures — This section must be completed for your vote to count. Please date and sign below.B q IF VOTING BY MAIL, SIGN, DETACH AND RETURN THE BOTTOM PORTION IN THE ENCLOSED ENVELOPE. q 2023 Special Meeting Proxy Card Proposals — The Board of Directors recommends a vote FOR Proposals 1, 2 and 3.A 1. To approve the Agreement and Plan of Reorganization and accompanying Plan of Merger, dated as of August 24, 2023 (the “merger agreement”), by and between Burke & Herbert Financial Services Corp. (“Burke & Herbert”) and Summit Financial Group, Inc. (“Summit”), and the other transactions contemplated by the merger agreement, pursuant to which Summit will merge with and into Burke & Herbert as more fully described in the accompanying joint proxy statement/prospectus. For Against Abstain For Against Abstain 3. To adjourn the Summit special meeting, if necessary or appropriate, to solicit additional proxies if, immediately prior to such adjournment, there are not sufficient votes to approve the Summit merger proposal or to ensure that any supplement or amendment to the accompanying joint proxy statement/prospectus is timely provided to holders of Summit common stock. Note: Consummation of the merger and other transactions contemplated by the merger agreement is not conditioned on Proposal 3. IF THIS PROXY IS PROPERLY SIGNED AND IS NOT REVOKED, THIS PROXY WILL BE VOTED AS DIRECTED, BUT IF NO INSTRUCTIONS ARE SPECIFIED, THIS PROXY WILL BE VOTED FOR APPROVAL OF ALL PROPOSALS. IF ANY OTHER BUSINESS IS PROPERLY PRESENTED AT THE MEETING, OR ANY ADJOURNMENT OR POSTPONEMENT THEREOF, THIS PROXY WILL BE VOTED BY THOSE NAMED IN THIS PROXY IN THEIR BEST JUDGMENT. 2. To approve, on an advisory (non-binding) basis, the merger-related compensation payments that will or may be paid to the named executive officers of Summit in connection with the transactions contemplated by the merger agreement. For Against Abstain M M M M M M M M M 5 9 0 5 6 6 MMMMMMMMMMMM

Using a black ink pen, mark your votes with an X as shown in this example. Please do not write outside the designated areas. 2023 Special Meeting Proxy Card A Proposals - The Board of Directors recommends a vote FOR Proposals 1, 2 and 3. For Against Abstain For Against Abstain B Authorized Signatures - This section must be completed for your vote to count. Please date and sign below. SIGN, DETACH AND RETURN THE BOTTOM PORTION IN THE ENCLOSED ENVELOPE +1. To approve the Agreement and Plan of Reorganization and accompanying Plan of Merger, dated as of August 24, 2023 (the “merger agreement”), by and between Burke & Herbert Financial Services Corp. (“Burke & Herbert”) and Summit Financial Group, Inc. (“Summit”), and the other transactions contemplated by the merger agreement, pursuant to which Summit will merge with and into Burke & Herbert as more fully described in the accompanying joint proxy statement/prospectus. 3. To adjourn the Summit special meeting, if necessary or appropriate, to solicit additional proxies if, immediately prior to such adjournment, there are not sufficient votes to approve the Summit merger proposal or to ensure that any supplement or amendment to the accompanying joint proxy statement/prospectus is timely provided to holders of Summit common stock. 2. To approve, on an advisory (non-binding) basis, the merger- related compensation payments that will or may be paid to the named executive officers of Summit in connection with the transactions contemplated by the merger agreement. Please sign exactly as name(s) appears hereon. Joint owners should each sign. When signing as attorney, executor, administrator, corporate officer, trustee, guardian, or custodian, please give full title. Date (mm/dd/yyyy) — Please print date below. Signature 1 — Please keep signature within the box. Signature 2 — Please keep signature within the box. + For Against Abstain NOTE: CONSUMMATION OF THE MERGER AND OTHER TRANSACTIONS CONTEMPLATED BY THE MERGER AGREEMENT IS NOT CONDITIONED ON PROPOSAL 3. IF ANY OTHER BUSINESS IS PROPERLY PRESENTED AT THE MEETING, OR ANY ADJOURNMENT OR POSTPONEMENT THEREOF, THIS PROXY WILL BE VOTED BY THOSE NAMED IN THIS PROXY IN THEIR BEST JUDGMENT. PLEASE MARK, DATE, SIGN AND RETURN IMMEDIATELY. THE TRUSTEES MUST RECEIVE YOUR DIRECTION NO LATER THAN THE CLOSE OF BUSINESS (5:00 PM EASTERN TIME) ON NOVEMBER 29, 2023. FAILURE BY YOU TO PROVIDE DIRECTION TO THE TRUSTEES ON THIS FORM WILL RESULT IN THE TRUSTEES VOTING YOUR SHARES BASED ON THE TRUSTEES’ FIDUCIARY DISCRETION, WHICH MAY THEREFORE RESULT IN EITHER A “FOR” OR “AGAINST” VOTE. If you received this proxy card through electronic delivery, please mail the proxy card to the following address so as to arrive prior to November 29, 2023: Summit Financial Group, Inc. 300 N. Main Street Moorefield, West Virginia 26836 Attention: ESOP Trustees

IMPORTANT NOTICE REGARDING THE AVAILABILITY OF PROXY MATERIALS FOR THE SPECIAL MEETING OF SHAREHOLDERS TO BE HELD ON DECEMBER 6, 2023 2023 Special Meeting of Summit Financial Group, Inc. Shareholders will be held on December 6, 2023, 1:00 p.m. ET at Summit Financial Group, Inc. Headquarters 300 North Main Street, Moorefield, WV 26836 SIGN, DETACH AND RETURN THE BOTTOM PORTION IN THE ENCLOSED ENVELOPE CONFIDENTIAL VOTING INSTRUCTIONS - SUMMIT FINANCIAL GROUP, INC. + DIRECTION TO TRUSTEES OF SUMMIT FINANCIAL GROUP, INC. EMPLOYER STOCK OWNERSHIP PLAN RELATING TO THE SPECIAL MEETING OF THE SHAREHOLDERS ON DECEMBER 6, 2023 The undersigned participant in or, if applicable, beneficiary under, the Summit Financial Group, Inc. Employer Stock Ownership Plan (“ESOP” or “Plan”) does hereby direct the Trustees of the ESOP to vote the shares of Summit Financial Group, Inc. common stock allocated to his or her account(s) in the ESOP as follows: The Trustees will follow the directions of each Participant with respect to the voting of the whole and fractional shares of Summit Financial Group, Inc. common stock held in such Participant’s Plan Account, provided that such directions are received by the Trustees by 5:00 p.m. Eastern Time on November 29, 2023. Any such direction by a Participant to the Trustees shall be effective as of the date such direction is received by the Trustees. Each Participant shall be permitted to revoke or change such direction, provided such revocation or change is received by the Trustees by 5:00 p.m. Eastern Time on November 29, 2023. The Board of Directors recommends a vote “FOR” Proposals 1, 2 and 3. If no direction is given by a Participant, the Trustees are permitted to vote the shares allocated to such Participant’s Plan Account in the exercise of the Trustees’ fiduciary discretion. (Continued and to be marked, dated a signed, on the other side) C Non-Voting Items Change of Address — Please print new address below. Comments — Please print your comments below. +