SPECIMEN UNIT CERTIFICATE

Exhibit 4.13

SPECIMEN UNIT CERTIFICATE

[            ] UNITS

NUMBER U-[·]

SEE REVERSE FOR CERTAIN

DEFINITIONS

CERECOR INC.

CUSIP 15671L 208

UNITS CONSISTING OF ONE SHARE OF COMMON STOCK, A CLASS A WARRANT TO PURCHASE ONE SHARE OF COMMON STOCK AND A CLASS B WARRANT TO PURCHASE ONE HALF OF A SHARE OF COMMON STOCK

Each Unit (“Unit”) consists of one (1) share of common stock, par value $0.001 per share (“Common Stock”), of CERECOR INC., a Delaware corporation (the “Company”), a Class A Warrant and a Class B Warrant (together, the “Warrants”). Each Class A Warrant entitles the holder to purchase one (1) share of Common Stock for $[   ] per share (subject to adjustment). Each Class B Warrant entitles the holder to purchase one half (0.5) of a share of Common Stock for $[   ] per full share (subject to adjustment). Each Warrant will become exercisable on the date when the Units detach and the components begin to trade separately (as described in more detail below). Each Class A Warrant will expire unless exercised before 5:00 p.m. New York City time on the date which is thirty-six months from the date of the closing of the Company’s initial public offering or earlier upon redemption by the Company and each Class B Warrant will expire unless exercised before 5:00 p.m. New York City time on the date which is eighteen months from the date of the closing of the Company’s initial public offering (in each case, as applicable, the “Expiration Date”).

The Common Stock and Warrants comprising each Unit shall begin to trade separately on the first trading day following the sixtieth (60th) day after the effectiveness of the Registration Statement (or earlier, in the discretion of Maxim Group, LLC as representative of the underwriters); provided, however, in no event will the Common Stock and Warrants begin to trade separately until the Company issues a press release announcing when such separate trading will begin.

The terms of the Class A Warrants are governed by a Class A Warrant Agreement, dated as of [                    ], 2015, between the Company and American Stock Transfer & Trust Company, as Warrant Agent, and are subject to the terms and provisions contained therein, all of which terms and provisions the holder of this certificate consents to by acceptance hereof. The terms of the Class B Warrants are governed by a Class B Warrant Agreement, dated as of [                    ], 2015, between the Company and American Stock Transfer & Trust Company, as Warrant Agent, and are subject to the terms and provisions contained therein, all of which terms and provisions the holder of this certificate consents to by acceptance hereof. Copies of the Class A Warrant Agreement and the Class B Warrant Agreement are on file at the office of the Warrant Agent at 6201 15th Avenue Brooklyn, New York 11219, and are available to any Warrant holder on written request and without cost.

This certificate is not valid unless countersigned by the Transfer Agent and Registrar of the Company.

Witness the facsimile seal of the Company and the facsimile signature of its duly authorized officers.

[CERECOR INC.]

COUNTERSIGNED AND REGISTERED:

AMERICAN STOCK TRANSFER & TRUST COMPANY

TRANSFER AGENT AND REGISTRAR

[REVERSE OF CERTIFICATE]

CERECOR INC.

The Company will furnish without charge to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating, optional or other special rights of each class of shares or series thereof of the Company and the qualifications, limitations, or restrictions of such preferences and/or rights. This certificate and the units represented hereby are issued and shall be held subject to the terms and conditions applicable to the securities underlying and comprising the units, including, as applicable, the Certificate of Incorporation and all amendments thereto, the Bylaws, the Warrant Agreements and resolutions of the Board of Directors providing for the issue of securities (copies of which may be obtained from the secretary of the Company), to all of which the holder(s) of this certificate by acceptance hereof assents.

The following abbreviations, when used in the inscription on the face of this certificate, shall be construed as though they were written out in full according to applicable laws or regulations:

TEN COM — as tenants in common

TEN ENT — as tenants by the entireties

JT TEN — as joint tenants with right of survivorship and not as tenants in common

UNIF GIFT MIN ACT— Custodian

(Cust) (Minor)

under Uniform Gifts to Minors Act

(State)

Additional abbreviations may also be used though not in the above list.

For value received, hereby sell(s), assign(s) and transfer(s) unto

PLEASE INSERT SOCIAL SECURITY OR OTHER IDENTIFYING NUMBER OF ASSIGNEE(S)

(PLEASE PRINT OR TYPEWRITE NAME(S) AND ADDRESS(ES), INCLUDING ZIP CODE, OF ASSIGNEE(S))

Units represented by the within Certificate, and hereby irrevocably constitute(s) and appoint(s) Attorney to transfer the said Units on the books of the within named Company with full power of substitution in the premises.

Dated:

NOTICE: THE SIGNATURE(S) TO THIS ASSIGNMENT MUST CORRESPOND WITH THE NAME AS WRITTEN UPON THE FACE OF THE CERTIFICATE IN EVERY PARTICULAR, WITHOUT ALTERATION OR ENLARGEMENT OR ANY CHANGE WHATEVER.

Signature(s) Guaranteed:

By

THE SIGNATURE(S) MUST BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM, PURSUANT TO S.E.C. RULE 17Ad-15).