Royal Caribbean advertises that they have a fitness center, including free weights, on all their ships.
On the Viking Serenade, the "fitness center" consists of a few cardio machines in a hallway. No free weights, no resistance machines. I was frustrated because I like to use weights on a regular basis, so I wasn't able to lift for a week.
So the only way you can tell for sure is if someone who was on that specific ship posts a report, or find out when you get on board.