I haven't ever missed the boat, though I know people who have (that's another story).
When I was working on the Norway in 93 I was standing on the pier talking to my girlfriend on the payphone. Suddenly I realized I hadn't checked the time so I looked at my watch and I saw I was 10 minutes past the cut-off time (1/2 hour before sailtime).
Well, they are sticklers for the crew, so I ran to the crea gangway - and it was up! The staff officer was on the ship looking out at me, there was a 6-foot gap of water between us. I said "What should I do, jump it?" and he said "no, you're too late." I said "What? I have to sail, I work here, they need me." He said "what do you do?"
"stage manager in the Cabaret lounge" (I think we thought I might be a waiter, I look sort of eastern European).
"well, you're too late and you can't jump"
"this is really bad, no one can replace me, only I know the system."
"well, go to the passenger gangway and give the security officer your crew card"
and with that he radioed the passenger gangway, which I hadn't even noticed was still out. I ran through the terminal, up 3 decks and crossed over to the ship. The security officer stopped me and comfiscated my crew card, he said "you can pick this up in the staff captain's office tomorrow"
When I went to the staff captain's office I got more than a lecture -- I WAS GROUNDED! They would not let me off the ship for the next week's cruise! It was so funny I felt like I was 12 years old again.