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 quarterly report of Safety Insurance Group, Inc. (the “Company”) on Form 10-Q for the period ending March 31, 2024 as filed with the United States Securities and Exchange Commission on the date hereof (the “Report”), I, George M. Murphy, President, Chief Executive Officer and Director 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, Chief Executive Officer and Director

(Principal Executive Officer)

May 9, 2024