Given the number of people on cruise ships at any given time, it's reasonable to expect there is a need to reach a passenger when they're at sea.
Such emergencies can be dealt with by calling the cruise line and finding out how to reach somebody on a specific ship, assuming you know the specific ship.
But if nobody is answering the cruise line's phone in the middle of the night when you need 
to call, here's what you do:
Go to www.dialaship.com.
This service, which is not free, is operated by MTN. That's the company that provides satellite communications to cruise ships around the world. Also not free — as you know if you've used the Internet while on a cruise.
The first click takes you to a lengthy list of cruise ships, categorized by cruise line. There is a 1-800 number to call for that ship (so far, it's still free). Then a computerized voice will prompt you to enter the ship's name and, before the connection is made, you also have to enter a credit card number (this is where it stops being free). The meter begins to run once an automatic system or live operator answers, presumably on the ship you're calling.
What's the cost?
If it's an emergency, does it really matter?
Royal Caribbean Majesty of the Seas
3 nights
January 4, 2013
Miami (return): Coco Cay, Nassau
Inside: $219
Cost per day: $73
www.royalcaribbean.com