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You won't be able to invite any guests aboard your cruise ship. Only passengers with valid seaboard passcards will not allowed through the security
checks. Your seaboard passcard is your only passport to access on & off the cruise ship.
Most ships now have much tighter security and the answer is no but you should enquire at the Guest Relations desk to see if your ship will allow but if you do want to do this do it well in advance and not the night befor.
The two earlier answers are generally correct, BUT not so in every case. . .
I wrote a lengthy answer a few days back to the query regarding my favourite ship. The CRYSTAL SYMPHONY it is. And now, another reason why CRYSTAL is such a helpful cruise line: they allow me to have guests visit me in port. I have done it twice. The first time in San Frnacisco. I invited my "best man" and his wife; the second time in Miami my guests were my sister, her husband and their son and daughter-in-law. The cruise line however requires me to send them certain details of the visitors some 20 days in advance, viz. their names, birthdates, Vehicle Driver ID numbers, and current address. Which is OK by me and my guests. So, once again, (I do assure you that I do not own any stock in CRYSTAL) I highly recommend that line for warm, friendly, efficient cruising!
Kobad Arjani (firstname.lastname@example.org)