Exhibit 32.1

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 Safety Insurance Group, Inc. (the “Company”) on Form 10-K for the period ending December 31, 2023 as filed with the United States Securities and Exchange Commission on the date hereof (the “Report”), I, George M. Murphy, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

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

 • The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of and for the periods presented in the Report.

 /s/ GEORGE M. MURPHY

 George M. Murphy

President and Chief Executive Officer
February 28, 2024