If you can do so, wait 'til you board the ship. When you get on board, ask the crew what phone card they use. You can buy them in any port. Since many if the ship's staff call family/friends when in port, they should be able to "point you in the right direction". Also, if possible, wait 'til later in the day to phone your parents. Earlier, those phones will be in use by the crew.
Many "phone cards" you buy locally won't work in the ports.