Call the cruiseline! They may be able to tell you. It's public record. If that fails, call the cruiseline as if you were getting married. Find out where the licenses, etc. have to be filed (possibly in your home city). Knowing this, you could then go to where the records are kept (probably their local city/county records office) and look up the marriage license.
My daughter was married this June on the Raphdosy of the Sea docked in Galveston, Tx.
It was a lovely wedding. the only problem we have is we can not get the marriage licence. we have called Royal Romance several times and the are giving us the run around. They are not helping us one bit. They will not let us talk to a supervisor and will not give us the phone number of the minister that married them. Does any one have any suggestions on what to do?