Well, if a cruise line told me I may need to show a marriage license I'd make sure I brought it with me. Do you really want to gamble on this? Better to have it and not need it than to have the opposite happen, which means you won't be allowed to board.
Within the next two years you will need a passport. If you have time before your next cruise I strongly urge you to get a passport. You should be able to get a copy of a marriage license from the state, county, city which issued the original.