We use a waterproof wallet, and while we've had one that leaked a little when we took it scuba diving, it was not a problem since all we put in it was our drivers license, ship card, credit card, a reduced sized copy of the photo page of our passport that had been laminated and a little cash. I generally loop the cord through the strap of my swimsuit and wear it around my neck, that way I know I won't lose it and it is inconspicuous under my clothes.
Here's what they look like. You can often find them onboard the ship in the gift shop and also in dive shops. I don't like the thought of leaving anything valuable sitting on the beach, while I am in the water. There are flatter styles which I like better than this one, but they don't hold as much.