The only thing I ever recommend is that you write the person's name, job title and "c/o ship name" on an envelope and mail a letter to the cruise line's head office.
c/o Carnival Conquest
Carnival Cruise Lines
3655 NW 87th Avenue Miami, FL 33178
This is essentially the same way that relatives communicate with loved ones on cruise ships. (you can leave off the job title)
That letter should reach the intended recipient although it will take awhile.
It is hard for some people to understand, I suppose, that it is probably better not to let crew members get under your skin, but we do not know why this person wants to contact this person. Maybe he's a daddy? (I know, that's not that funny, but you never know).
Anyway - as said, if you leave a ship without getting the contact information you are seeking, chances are that person did not want to hear from you. If you still want to contact them, you can write a letter as I described.