Exhibit 4.1

C O M M O N S T O C K OCEAN RIG UDW INC. SEE REVERSE FOR CERTAIN DEFINITIONS OF INCORPORATED UNDER THE LAWS OF THE REPUBLIC OF THE MARSHALL ISLANDS CUSIP Y64354 20 5 1,000,000,000 Shares — Par Value $0.01 each Common Stock 500,000,000 Shares — Par Value $0.01 each Preferred Stock THIS cerTIfIeS THAT IS THe owner of FULLY PAID AND NON-ASSESSABLE SHARES OF THE PAR VALUE OF $0.01 EACH OF THE COMMON STOCK OF OCEAN RIG UDW INC. BY transferable on the books of the Corporation in person or by duly authorized attorney upon surrender of this certificate properly endorsed. This certificate is not valid unless countersigned by the Transfer Agent and registered by the Registrar. Witness the AMERICAN facsimile seal of the Corporation and the facsimile signatures of its duly authorized officers. COUNTERSIgNED STOCKAND Dated: (New TRANSFER REgISTERED: York, I G            R U . N& Y D ) . N W A TRUST E I MARSHALL C N            ISLANDS C O . AUTHORIzED AND COMPANY, TRANSFER LLC PRESIDENT AND CHIEF EXECUTIVE OFFICER SECRETARY SIgNATURE REgISTRAR AgENT

OCEAN RIG UDW INC. 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 UNIF GIFT MIN ACT— Custodian — (Cust) (Minor) TEN ENT as tenants by the entireties under Uniform Gifts to Minors JT TEN — as joint tenants with right of survivorship and not as tenants Act (State) in common Additional Abbreviations may also be used though not in the above list. For Valued Received, hereby sell, assign and transfer unto PLEASE INSERT SOCIAL SECURITY OR OTHER IDENTIFYING NUMBER OF ASSIGNEE (PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE) Shares of the capital stock represented by the within Certificate, and do hereby irrevocably constitute and appoint Attorney to transfer the said stock on the books of the within named Corporation with full power of substitution in the premises. Dated NOTICE: The signature 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: 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). THIS CERTIFICATE ALSO EVIDENCES AND ENTITLES THE HOLDER HEREOF TO CERTAIN RIGHTS AS SET FORTH IN AN AMENDED AND RESTATED STOCKHOLDERS RIGHTS AGREEMENT BETWEEN OCEAN RIG UDW INC. AND AMERICAN STOCK TRANSFER & TRUST COMPANY, LLC AS THE RIGHTS AGENT, DATED AS OF JUNE 3, 2011 (THE “RIGHTS AGREEMENT”), THE TERMS OF WHICH ARE HEREBY INCORPORATED HEREIN BY REFERENCE AND A COPY OF WHICH IS ON FILE AT THE PRINCIPAL EXECUTIVE OFFICES OF OCEAN RIG UDW INC. UNDER CERTAIN CIRCUMSTANCES, AS SET FORTH IN THE RIGHTS AGREEMENT, SUCH RIGHTS WILL BE EVIDENCED BY SEPARATE CERTIFICATES AND WILL NO LONGER BE EVIDENCED BY THIS CERTIFICATE. OCEAN RIG UDW INC. WILL MAIL TO THE HOLDER OF THIS CERTIFICATE A COPY OF THE RIGHTS AGREEMENT WITHOUT CHARGE AFTER RECEIPT OF A WRITTEN REQUEST THEREFOR. UNDER CERTAIN CIRCUMSTANCES SET FORTH IN THE RIGHTS AGREEMENT, RIGHTS ISSUED TO, OR HELD BY, ANY PERSON WHO IS, WAS OR BECOMES AN ACQUIRING PERSON OR ANY AFFILIATE OR ASSOCIATE THEREOF (AS SUCH TERMS ARE DEFINED IN THE RIGHTS AGREEMENT), WHETHER CURRENTLY HELD BY OR ON BEHALF OF SUCH PERSON OR BY ANY SUBSEQUENT HOLDER, MAY BECOME NULL AND VOID.