First of all when you are cruising it's a ship not a boat. Recently there was an incident reported of a woman who missed the ship's sailing time. The media played on the fact that her children were still on board the ship. As you can see in the Inside Edition report the children were just fine. It was decided when the woman did not show up at sailing time that the husband would leave the kids with an uncle and go ashore with passports in hand and try to find the woman who apparently was shopping. The ship waited a half hour past departure time and then left with the woman and her husband frantically running down the dock.
We often stand and watch as the ship departs the port. There is always someone running at the last minute to catch their ride before the gangway is pulled in. We have even seen some captains go above and beyond. One pulled back the few feet that the ship had moved. Another dropped one of the small boats the crew uses to paint and repair around the ship's exterior and picked up a passenger. Her name was mentioned every day for the rest of the cruise when the captain or cruise director reminded people of departure time. We suspect she was charged for the extra service.
Another time we watched two men run for the ship. Their passports had been pulled and sent ashore with shore authorities and as we pulled away we could see the authorities hand them the passports. They threw their hands in the air in despair as they were told to meet us in the next port.
Unless you like to live on the edge, you need to be aware of the time all passengers are expected back on board. It is always a half hour before departure. A ship will usually wait a short period of time for a missing passenger but they have a schedule to keep and I suspect they get charged for being at the pier longer than scheduled. After all, the dock workers have to be paid for extra time, port authorities have to hang around, etc.
Be sure to check your watch against local time. Make sure you are operating in the same time zone as the ship which is always the local time on shore.
Anyone on a ship's excursion is guaranteed to make it back to the ship before it sails. The ship will wait for a delayed ship's excursion. But if you are off on your own excursion, better be sure that you allow for time to return. Some ports like Charlotte Amalie in St. Thomas have horrendous traffic jams made more difficult when there are several ships in port and everyone is trying to get back at the same time.
Plan wisely Grasshopper and don't be like the White Rabbit--Late!