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You don't say who you are going with, but if it's a US cruise line you should be able to cash them on board at the Pursers Desk at no charge. Check their brochure or web site to ensure they will cash them. I also believe Costa and MSC as USD based out there but may not encash T/C's. Island based banks will probably want to exchange them into local currency and charge you commission. The problem then is that the local shops will probably prefer US Dollars so you then have the problem of what to do with the local currency. US banks based on the islands may change them for you but generally they don't like to and you will need plenty of ID when you go in. Depending on where you go to there may be some local currency exchange shops but they are there to make a profit. Personally I can think of better things to do when visiting a Caribbean island than queue up in a bank.
Thank you for your answer - We are sailing on a UK£ ship (the Island Star). I agree I don't want to queue at a bank. Are there any problems using them for car hire or retail therapy?
Most car hire companies would require a credit card so that they can charge you for any damage they may find after you have dropped the car off or fuel you haven't replaced. You may be able to use them at some of the diamond and jewellry stores in the americanised shoping malls that are on some of the islands. You may also be able to encash them on Island Star as they will keep USD at the Pursers desk but only they could confirm that, otherwise I recall there is an exchange bureau at Barbados port (in the port side shopping mall). A lot of US ships call in there so you may be able to get dollar bills from them. Hope this helps. Have a nice cruise.