Verizon has a feature you can add called Travel Pass that may give you access while in port. It is $10 for 24 hours and is supposed to provide you the same plan you have at home. You don't pay until it is activated and it is activated on first use. I enabled it on my wife's phone prior to a cruise to Nassau and CC.
We found was it was better for voice than data and messaging. While in Nassau, we walked over to the Never Say Never Again Bar and Grill. It is the octagon building at the end of the pier on the left side of the Port Nassau web cam. We have been watching this place on the web cam since before it opened. We ordered a couple of mimosas, took some photos and had a nice long phone call with our daughter in NJ.
Data was unreliably slow and messaging had us wondering if the messages went through using Verizon's messaging app.
We tried messaging the next day at CC. Someone said if you time it correctly, it would be the same 24 hour period. After struggling to send a message to our daughter, I looked at the time and had the thought 'I wonder if that message just cost me another $10...', and called our daughter again. Had a nice call. Again, data and messaging were not great. But the call went through. Not a lot of bars on the signal strength where we were. Other locations may have been better.
I would recommend you disable all background activity and updates for your apps for both the on ship internet access and if you opt ot go with Travel Pass. Disable auto updates too. On the ship you can exhaust your free 50 MB, or other internet data plan, quickly if your apps are connecting in the background. Having only one phone accessing the free 50 MB worked well for a while for us. My wife did some messaging and some FB stuff. Then I took my phone out of airplane more and it was difficult to track our usage.
Your Verizon plan may cover some other countries. Their site can tell you where you can use travel pass.
There are posts regarding free imessage access on some
DCL ships. We're on Samsung so I haven't really been paying attention to the imessage stuff.