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

    We, Paul R. Edick and Steven M. Pieper, of Xeris Pharmaceuticals, Inc., certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, to the best of our knowledge, that:

1.    The quarterly report on Form 10-Q for the quarter ended June 30, 2021 (Periodic Report) to which this statement is an exhibit fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, and

2.    Information contained in the Periodic Report fairly presents, in all material aspects, the financial condition and results of operations of Xeris Pharmaceuticals, Inc.

Date: August 5, 2021

/s/ Paul R. Edick

Paul R. Edick

Chairman and Chief Executive Officer

(Principal Executive Officer)

/s/ Steven M. Pieper

Steven M. Pieper

Chief Financial Officer

(Principal Financial Officer)