If it is not a "right this second" emergency, email is a great way to stay in touch and you can check it regularly on board. Otherwise, there are phone numbers that can be called, but the cost is VERY, VERY EXPENSIVE.
the ship to shore costs are extremely high....there will be a phone number in your documents in case folks at home need to reach you....or you could set up an internet account onboard and they could reach you that way...you would just have to obviously check your messages.
The phone rates are at about $6.95 or so per minute.
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