You will need Euros in all Med ports, dollars for tips on board and paying onboard account if not paying by creditcard.
We buy our euros before we go., as exchange rate usually better on land than ship .
What ports are you doing? I did a Med cruise last summer , If doing Rome, go on a trip from the ship, as it is 1 1/2hrs away from the port, and trains are difficult - miss the train back and the ship sails without you!
We did a full day tour with a lunch included, and we were fast-tracked past the very long queues for the Vatican, Colosseum and Sistine Chapel - we also saw the St Peters Basilica, Roman Forum and Trevi Fountain all in one day in 90 degree heat! A hot tiring day , but worth doing if you have never been to Rome before.
The problem with Traveller checks is that its very hard to convert them in cash as stores usually will not accept them (in Europe). This means you need to change them on board or at a bank.
February 2008: HAL Zuiderdam: Eastern Caribbean
November 2009: HAL Noordam: Caribbean Wayfarer
November 2010: Norwegian Jade: Western Mediterranean
January 2012: HAL Eurodam: Eastern Caribbean
May 2012 HAL: Noordam: Transatlantic Riviera