Yes, most cruise ships are insured with Lloyds of London. These policies are expensive however and of course they are very specialized. Like any business there will be some fallbacks that the company just chooses to "eat the loss"
The Lloyds insurance would be more likely to kick in if there was a catatrophic loss of a $1billion vessel and thousands of lives. The kind of event that would make a cruise line go bankrupt.
What just happened to Carnival is a blip and probably will not impact earnings that much. The line has 23 ships and carries over 100,000 passengers every week.
All they are giving away is a few free cruises. Thank God and our government for the Navy, though, and the Coast Guard. People do not realize how much the Coast Guard does for us on a daily basis.