My wife is traveling overseas and had to work this out as well. So, here's the story.
Before you leave, login to your Verizon account and add the feature for Global Roaming. Once overseas, you can set your mobile network to Global. Provided Verizon has a roaming agreement there, you can call and use data. Charges are very high though. The cruise ship may already provide Verizon service though, so I'd check with them before you do anything.
Another option is to use a foreign sim card. Depending on how often you plan to use your phone, it could lower your costs dramaticly. Being that you're on a cruise ship , I don't know if it would help. The one issue with foreign sims is that data will most likely not work. You need to enter a new APN into your phone to connect to a foreign carrier data plan. The GS3 for some reason doesn't let you change from the Verizon APN. It's possible to change it, but you have to roote the phone and the process is a little involved. So you'll probably still need to rely on wifi for data if you go this route.
Another option is to just use wifi only. If you have a Google Voice app and account, you can call the U.S. for $0.01/minute. It may use Verizon plan minutes on your regular phone dialier. You can use Talkatone as your dailer to avoid using plan minutes. Be aware that the ship may charge you for wifi.