This is a very popular activity, and you can have a romantic wedding with as
many -- or few -- frills as you like. Carnival doesn't offer weddings at sea, but it's a cinch to tie the knot aboard the ship's in home port (mostly Miami), before you leave. Then, you have your honeymoon aboard ship.
One company arranges all the wedding details, including license, for nearly every cruise line: A Wedding For You. Their web site: http://www.aweddingforyou.com
. You can also get married in several ports, including St. Thomas. But these folks are the best, and I'd go directly to them.