What happens if you're not on-board your cruise ship at a mid-cruise stopover, and the ship is ready to depart?

It happens. It's sad to see guests running along the pier as the ship departs. If you miss the ship, you must find alternative transport to meet the ship at it's next port. The ship will wait for latecomers if they are on an excursion sold by the ship. Tip:  always note the name and contact info for the port agent listed in the daily newsletter from the ship.  Contact that person if you are late to return to the ship.  Rarely, the port agent can pursuade the ship to delay for a few minutes.  Otherwise, the port agent can help you reach the next port.

Same thing in the Navy, except you also get in huge trouble.  You lose fewer points if you hire a boat or helicopter to overtake and transfer aboard.  On a cruise ship I'm sure they don't want to see you at that point until the next port.

It actually depends on the ships schedule, the time it can be on port (if there is another ship coming to that particular pier or not, if it’s a tight itinerary, etc) remember some ports have a schedule for ships to go in & out and if the ship is delayed for any reason it misses it’s spot it will have to wait for the next spot available one (and of course charges apply).Most cruise lines I been will wait for you few minutes (5, 10 or 15 but no more) … unless is a ship’s tour, then the ship will wait for you or in the worst scenario cover the expenses to the next port but remember the ships tour won’t wait for you more than few minutes either.But before the ship will departure many things happen onboard, there will make announcements asking the “missing” guest to contact reception, security or housekeeping will check the cabins, the hotel officer’s will do a ship’s search in public areas and basically double check if is not a gangway or system failure and the guest are actually are onboard and the ship it’s been delayed for not reason, now at the same time if the passports are with the Purser’s office, the immigration purser will wait to the last minute possible to land them and give them to the ship’s agent along with a disembarking guest list, after that the gangway is pull out and arrivederci, see you next port.The guests will then have to make their own way to the next port of call to meet the ship at their own expense of course... I have seen a couple times, guests trying to catch the ship hiring a boat or with the pilot boat, but so far I have never seen any captain let the guest embark that way (due to safety and security reasons).

The ships will leave you. Then you will run down the pier screaming and flailing your arms and people will stand at the railing of the ship and laugh at you. The people who do this are called “pier runners,” and many veteran cruisers make a hobby out of watching them. If the ship leaves you, you will have to embark at the next port.

Depending on the captain and schedule the ship might wait for a little while and see if the missing guest(s) turn up.If they don’t then the passports will be landed with the local ship’s agent and a representative of the agency usually waits at the pier to meet the guests once they show up.The guests will then have to make their own way to the next port of call to meet the ship - at their own expense.That happened once on the cruise ship I was working on… we had had a time change the night before and the guests had missed to change their watches.