Specimen Unit Certificate

Exhibit 4.1

SPECIMEN UNIT CERTIFICATE

ARCHIMEDES TECH SPAC PARTNERS II CO.

UNITS CONSISTING OF ONE ORDINARY SHARE AND

ONE-HALF OF ONE REDEEMABLE WARRANT TO PURCHASE ONE ORDINARY SHARE

Each Unit (“Unit”) consists of one (1) ordinary share, par value $0.0001 per share (“Ordinary Share”), of Archimedes Tech SPAC Partners II Co., a Cayman Islands exempted company (the “Company”), and one-half (1/2) of one redeemable warrant (each whole warrant, a “Warrant”). Each whole Warrant entitles the holder to purchase one (1) Ordinary Share (subject to adjustment) for $11.50 per share (subject to adjustment). Each Warrant will become exercisable on the later of (i) thirty (30) days after the Company’s completion of a merger, share exchange, asset acquisition, share purchase, reorganization or other similar business combination with one or more businesses (each a “Business Combination”), and (ii) twelve (12) months from the closing of the Company’s initial public offering, and will expire unless exercised before 5:00 p.m., New York City Time, on the date that is five (5) years after the date on which the Company completes its initial Business Combination, or earlier upon redemption or liquidation. The Ordinary Shares and Warrants comprising the Units represented by this certificate are not transferable separately prior the 52nd day following the date of the Company’s initial public offering unless BTIG, LLC, the representative of the underwriters of the Company’s initial public offering, elects to allow earlier separate trading, subject to the Company’s filing of a Current Report on Form 8-K with the Securities and Exchange Commission containing an audited balance sheet reflecting the Company’s receipt of the gross proceeds of its initial public offering and issuing a press release announcing when separate trading will begin.

The terms of the Warrants are governed by a Warrant Agreement, dated as of            , 2024, between the Company and Odyssey Transfer and 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 Warrant Agreement are on file at the office of the warrant agent at 2155 Woodlane Drive, Suite 100, Woodbury, MN 55125, 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 registered by the Registrar of the Company.

This certificate shall be governed by and construed in accordance with the internal laws of the State of New York, without regard to conflicts of laws principles thereof.

Witness the electronic or facsimile signatures of its duly authorized officers.

ARCHIMEDES TECH SPAC PARTNERS II CO.

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.

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:

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

represented by the within Certificate, and do(es) hereby irrevocably constitute and appoint

Attorney to transfer the said Units on the books of the within named Company with full power of substitution in the premises.

Dated                                                                     

In each case, as more fully described in the Company’s final prospectus dated         , 2024, the holder(s) of this certificate shall be entitled to receive a pro-rata portion of certain funds held in the trust account established in connection with the Company’s initial public offering only in the event that (i) the Company redeems the Ordinary Shares sold in its initial public offering and liquidates because it does not consummate an initial business combination within the completion window, as set forth in the Company’s amended and restated memorandum and articles of association, (ii) the Company redeems the Ordinary Shares sold in its initial public offering in connection with a shareholder vote to amend the Company’s amended and restated memorandum and articles of association (A) to modify the substance or timing of the Company’s obligation to allow redemption in connection with the Company’s initial business combination or redeem 100% of its Ordinary Shares sold in its initial public offering if it does not consummate an initial business combination within the completion window or (B) with respect to any other material provisions relating to shareholders’ rights or pre-initial business combination activity, or (iii) if the holder(s) seek(s) to redeem for cash his, her or its respective Ordinary Shares in connection with a tender offer (or proxy solicitation, solely in the event the Company seeks shareholder approval of the proposed initial business combination) setting forth the details of a proposed initial business combination. In no other circumstances shall the holder(s) have any right or interest of any kind in or to the trust account.