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 the Quarterly Report on Form 10-Q of Bowhead Specialty Holdings Inc. (the “Corporation”) for the period ended June 30, 2024 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Brad Mulcahey, Chief Financial Officer and Treasurer of the Corporation, 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:

1.    The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2.    The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Corporation.

Dated: August 8, 2024        

/s/ Brad Mulcahey
Brad Mulcahey
Chief Financial Officer and Treasurer      (Principal Financial Officer)