This is NOT what I would suggest but if you feel the need for 24/7 coverage then you would want to rent a satellite phone
. If it's a true EMERGENCY, then your sitter can call the ship and the front desk will find you. Yes, its expensive but in the case of a real emergency, money is not an issue. But, if all you want to do is call to see how junior is doing then, as an alternative, when you arrive in port, you can find any number of phone cards you can purchase to use on a public phone to call home.
Personally, I have a tri-mode mobile phone with service from T-Mobile. I can receive and place calls in most countries around the world and have used it from China to Africa to India. But, when you are at sea and out of range of the cell towers, it is only good as a paperweight! Some ships are beginning to add mobile coverage (e.g. RCI's Freedom of the Seas) on board.