CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with this Annual Report of Burke & Herbert Financial Services Corp. (“Burke & Herbert”) on Form 10-K for the year ending December 31, 2023 as filed with the Securities and Exchange Commission on the date hereof, I, Roy E. Halyama, Executive Vice President and Chief Financial Officer of Burke & Herbert, certify pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Form 10-K fairly presents, in all material respects, the financial condition and results of operations of Burke & Herbert.

By:	/s/ Roy E. Halyama
Name:	Roy E. Halyama
Title:	Executive Vice President and Chief Financial Officer

Date: March 22, 2024