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

Pursuant to the requirement set forth in Rule 13a-14(b) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and Section 1350 of Chapter 63 of Title 18 of the United States Code (18 U.S.C. §1350),Sandeep Kulkarni, Chief Executive Officer of Tourmaline Bio, Inc. (the “Company”), and Ryan Robinson, Interim Chief Financial Officer of the Company, each hereby certifies that, to the best of his knowledge:

1.The Company’s Annual Report on Form 10-K for the fiscal year ended December 31, 2023, to which this Certification is attached as Exhibit 32.1 (the “Annual Report”), fully complies with the requirements of Section 13(a) or Section 15(d) of the Exchange Act; and

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

In Witness Whereof, the undersigned have set their hands hereto as of March 19, 2024.

/s/ Sandeep Kulkarni	/s/ Ryan Robinson
Sandeep Kulkarni	Ryan Robinson
Chief Executive Officer (Principal Executive Officer)	Interim Chief Financial Officer, Vice President, Finance and Controller (Principal Financial Officer)

This certification accompanies the Form 10-K to which it relates, is not deemed filed with the Securities and Exchange Commission and is not to be incorporated by reference into any filing of Tourmaline Bio, Inc. under the Securities Act of 1933, as amended, or the Exchange Act (whether made before or after the date of the Form 10-K), irrespective of any general incorporation language contained in such filing.