Exhibit (a)(1)(H)

FORM OF EMAIL TO ELIGIBLE HOLDERS

CONFIRMING ACCEPTANCE OF ELIGIBLE OPTIONS

From:    Xeris Pharmaceuticals, Inc.

Re: Confirmation of Acceptance of Eligible Options

Thank you for your submission of the Election Form pursuant to the Offer to Exchange Eligible Options for New Options, dated November 10, 2020 (the “Offer Documents”). With this letter, we confirm that Xeris Pharmaceuticals, Inc. (“Xeris”) has accepted the Eligible Options listed on your Election Form for exchange in the Exchange Offer. Subject to the terms and conditions of the Exchange Offer, as described in the Offer Documents, your Eligible Options will be cancelled and New Options will be granted to you. Your New Options will appear shortly in E*TRADE, and your stock option agreement(s) will be available for electronic acceptance. If you have included in your Election Form an election to tender any options for exchange that do not qualify as Eligible Options, such options will not be accepted by Xeris and will remain outstanding subject to their original terms following the expiration of the Exchange Offer. If you have any questions, please contact Jennifer Bozarth, at jbozarth@xerispharma.com.

Capitalized terms used but not otherwise defined herein shall have the meanings set forth in the Offer Documents.

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