Exhibit 99.4

VOTE BY INTERNET - www.proxyvote.com Use the Internet to transmit your voting instructions and for electronic delivery of information up until 11:59 p.m. Eastern Time on the day before the meeting date. Have your proxy card in hand when you access the web site and follow the instructions to obtain your records and to create an electronic voting instruction form. OCEAN RIG UDW INC. C/O OCEAN RIG CAYMAN MANAGEMENT SERVICES SEZC LIMITED 3RD FLOOR FLAGSHIP BUILDING HARBOUR DRIVE GRAND CAYMAN, CAYMAN ISLANDS ELECTRONIC DELIVERY OF FUTURE PROXY MATERIALS If you would like to reduce the costs incurred by our company in mailing proxy materials, you can consent to receiving all future proxy statements, proxy cards and annual reports electronically via e-mail or the Internet. To sign up for electronic delivery, please follow the instructions above to vote using the Internet and, when prompted, indicate that you agree to receive or access proxy materials electronically in future years. VOTE BY PHONE - 1-800-690-6903 Use any touch-tone telephone to transmit your voting instructions up until 11:59 p.m. Eastern Time on the day before the meeting date. Have your proxy card in hand when you call and then follow the instructions. VOTE BY MAIL Mark, sign and date your proxy card and return it in the postage-paid envelope we have provided or return it to Vote Processing, c/o Broadridge, 51 Mercedes Way, Edgewood, NY 11717. TO VOTE, MARK BLOCKS BELOW IN BLUE OR BLACK INK AS FOLLOWS: E51774-TBD KEEP THIS PORTION FOR YOUR RECORDS DETACH AND RETURN THIS PORTION ONLY THIS PROXY CARD IS VALID ONLY WHEN SIGNED AND DATED. OCEAN RIG UDW INC. The Board of Directors recommends you vote FOR proposals 1 and 2. For Against Abstain ! ! ! 1. Approval of a special resolution pursuant to the Cayman Islands Companies Law (2018 Revision) of the laws of the Cayman Islands and the Second Amended and Restated Memorandum and Articles of Association (the "Articles") of Ocean Rig UDW Inc. ("Ocean Rig") to approve the merger agreement, dated as of September 3, 2018 ( the "Merger Agreement"), by and among Ocean Rig, Transocean Ltd. ("Transocean"), Transocean Oceanus Holdings Limited, and Transocean Oceanus Limited ("Merger Sub"), and the transactions contemplated thereby, pursuant to which, among other things, Merger Sub will merge with and into Ocean Rig, and, following the merger, Ocean Rig will continue its corporate existence as the surviving corporation and will be a wholly-owned indirect subsidiary of Transocean. ! ! ! 2. Approval of adjournments of the Ocean Rig Extraordinary General Meeting, if necessary, to permit further solicitation of proxies if there are not sufficient votes at the time of the meeting to approve the Merger Agreement. Drag Along Election 1a. Election to be a Drag-Along Seller (as defined in the Articles) and to authorize the officers of Transocean to take all such actions to effect the transactions contemplated by the Merger Agreement as a Drag-Along Sale (as defined in the Articles) in accordance with Article 6.2.2 of the Articles, to the extent permitted thereunder and Transocean determines it is advisable to pursue a Drag-Along Sale, provided that in all cases the Merger Agreement has not been terminated in accordance with its terms. ! ! ! NOTE: Such other business as may properly come before the meeting or any adjournment thereof. Please sign exactly as your name(s) appear(s) hereon. When signing as attorney, executor, administrator, or other fiduciary, please give full title as such. Joint owners should each sign personally. All holders must sign. If a corporation or partnership, please sign in full corporate or partnership name by authorized officer. Signature [PLEASE SIGN WITHIN BOX] Date Signature (Joint Owners) Date

Important Notice Regarding the Availability of Proxy Materials for the Extraordinary General Meeting: The Notice and Proxy Statement is available at www.proxyvote.com. E51775-TBD OCEAN RIG UDW INC. Extraordinary General Meeting of Shareholders November 29, 2018 at 9:00 a.m., Local Time This proxy is solicited by the Board of Directors The shareholder(s) hereby appoint(s) Mr. Anthony Kandylidis or, failing him, Mr. Iraklis Sbarounis or, failing him, Mr. Pankaj Khanna or, failing him, the duly appointed chairman of the Extraordinary General Meeting, as their proxy, and hereby authorize(s) such person to represent and vote, as designated on the reverse side of this ballot, all of the common shares of OCEAN RIG UDW INC. (the "Company") that the shareholder(s) is/are entitled to vote at the Extraordinary General Meeting of Shareholders to be held at 3rd Floor Flagship Building, Harbour Drive, Grand Cayman, Cayman Islands on November 29, 2018 at 9:00 a.m., local time, and any adjournment or postponement thereof. This proxy, when properly executed, will be voted in the manner directed herein. If no such direction is made, this proxy will be voted in accordance with the Board of Directors' recommendations. In particular, if a shareholder submits a blank proxy, it will be considered an election by such shareholder to be a Drag-Along Seller if the Company ultimately seeks to treat the Merger as a Drag-Along Sale. Continued and to be signed on reverse side