Also check with your network provider, it can cost you to receive calls abroad as well as to make them; doesn't hurt to let them know you're going either and will be making calls from abroad. We tend to text if necessary rather than call.
If they are phoning your mobile from the UK, they just dial the number. Bear in mind they will only 'get you' when your ashore/docked/or close to the coast. If you want to phone them +44 & remove the Zero if your phoning a land line.
On NCL there is a mobile network link which will allow you access even at sea, but you have to ensure you are using a triband or quadband mobile and I am sure your sons will sort you out on that. It is better to text rather than speak and yes if they phone you then you will be paying so put plenty credit into your phone, but I am sure they will use text it is still the way to do it. The other way is the ship has wi-fi and terminals in various locations and you will have a ship's email address which you can ask their IT desk to activate for you. If you want to be lumbered with a laptop and you have one you can also use it, but it will have to be registered with their IT desk and they do have restrictions for the use of their system but they will explain all to you. As it is wi-fi this means it would work in your cabin, or out on deck but like someone said a good walk is spoiled by golf, I am beginning to think a good cruise could be spoilt with computers and I love to get away from them. [apologies to golfers].