In case anyone else comes here looking for the same...
You can contact Royal Caribbean guests 24 hrs a day by calling +1 888 724 7447 and following the prompts to specify the ship you need to contact. The cost is $7.95 USD per minute and each call is limited to 10 minutes in duration. Please note that Visa and MasterCard are the only accepted forms of payment for this service.
This is typically used in emergency situations since the cost in quite high and the call time is limited to 10 minutes.
For non-emergency situations email and txt messages can come in handy. If you have family preparing for a cruise setting up a communication preference and timeframe prior to their departure is always a good idea.