Exhibit 32.1

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER

AND PRINCIPAL FINANCIAL OFFICER

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 of Cerecor Inc. (the “Registrant”) on Form 10-Q for the three and nine months ended September 30, 2019 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Joseph M. Miller, Chief Financial Officer of the Registrant, hereby 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 Registrant.

Date: November 14, 2019	/s/    Joseph M. Miller
	Joseph M. Miller
	Chief Financial Officer
	(Registrant’s principal executive officer, principal financial officer and principal accounting officer)

The foregoing certifications are not deemed filed with the Securities and Exchange Commission for purposes of section 18 of the Securities Exchange Act of 1934, as amended (Exchange Act), and are not to be incorporated by reference into any filing ofCerecor Inc.under the Securities Act of 1933, as amended, or the Exchange Act, whether made before or after the date hereof, regardless of any general incorporation language in such filing.