Teresa Cowley, who is from Mickleover in Derby was last seen heading towards the deck of the Pride of Rotterdam ferry in the early hours of Friday.
After visiting a bar, Mrs Cowley and her husband returned to their cabin but the door key did not work.
Mr Cowley went to a reception area to resolve the problem, leaving his wife sitting outside the cabin.
Police say CCTV and witness accounts showed Mrs Cowley went alone to a sun lounge on the ship shortly after 1am on Friday. Mr Cowley, who is now believed to have returned to the UK, is said to be too upset to speak to the media about his wife's disappearance.