Train from port of Civitavecchia

It's a regional train. Buy it from a machine or person at the station, or download the Trenitalia app and buy it online. If doing this excursion on your own, be very mindful of which train you need to return on, and what the All Aboard time is. Arrival and departure times are not the same as All ashore and all aboard times.

The Search box top center will help you find multiple discussions of logistics and attractions for "one day in rome." Have you been on a cruise before? Do you use public transportation at home? I mean, so you have some experience with a three or four-seat ride back to the ship, where you have no control over the precise timing of anything?

Suppose there are 10 ships of 2000 in port, and 20% of passengers use the train. That means 4000 people will be on the last 4 trains back to Cvitavecchia.

This link is not strictly about your question, but it may be of some help to you:

https://community.ricksteves.com/travel-forum/italy/rome-airport-to-port-outside-of-rome

Thank you for your advice Cjean! I did try downloading the App from the Apple Store, but could not find it. Then went on line to find out why and apparently it’s not available in Canada anymore?? We are booking a tour that starts at 1:30, and runs for three hours, so I believe we have plenty of time to get back to the ship. I think they want you back on board 2 hours before departure; but that being said, I’ve been on the ship minutes before departure watching people running to get on board. I know ship waits if you book through them, but they are so expensive!

Good point Tim about the number of people using public transit. We are going in November and hoping the tourist numbers are down. Maybe we'll look at booking an earlier tour.
Kaypea

I trust you understand I made up those numbers. Remember you don't control when your exalted-class of cabins gets to exit the ship.

I also meant to refer to a 50 passenger city port-shuttle bus meeting the train, and how many taxis could possibly fit next to the train station. I don't know if some piers require a bus from inside the Cruise Terminal building, but our required Port Shuttle (port traffic circle to the pier, no Terminal, for small ship) waited 15 minutes to fill up. No A/C running during the wait, BTW.

Many people who drive everywhere overlook that the average "latency" of each and every segment of a public transportation trip is 50% of the scheduled service interval. Not counting a fire or a visit by the Pope. (We found the Pope in town when we arrived in Panama City for a cruise!)

We did walk from the train to the port perimeter traffic circle, but it was hot and long, and not obvious. Remember that ports have airport security these days.

The best ticket is a 5 zone BIRG ticket for 12 Euro. That covers your return train into Rome and all transport within Rome. Buy that at the station or from any ATAC sales agent- there is a Tabac in the centre of town, and one outside the station which sells them.

The NCL literature mentions being on board 2 hours before the ship leaves but in practice I have never had it be more than an hour..

I know ship waits if you book through them, but they are so expensive!

True, but not nearly as expensive as getting your party to the next port to catch up with the ship. We too have seen folks racing along the dock as the ship was pulling away. Having taken the train from the port to Rome and from Rome to the port, I think I'd spend the money for a ship excursion and eliminate the stress and hassle of doing it on my own. Just something to consider.

I doubt more than 4 or 5 cruise ships could dock at IT-CVV (this is Civitavecchia Port code, they have one like airports) at once, but the point made above is valid. There could be lots of people on those trains back to Civitavecchia. Regional trains have no reserved seats, so first come first served, if all seats are taken, you stand up, just like a subway. For your return back, I would consider a taxi from Rome. I think the cost is 140 euro for over 3 people. It's not too bad if there are multiple travelers in your party.

You didn’t mention what day you were going, but definitely check out how many ships are going to be in port the day you dock. https://www.cruisetimetables.com/civitavecchia-rome-italy-cruise-ship-schedule.html
One time when I docked there in 2018, there were over 25,000 passengers on the same day!! On days like that, it can be very difficult to get a seat on the train.
We did the cruise excursion and did not regret it. It is a good hour and a half drive to and from the city, traffic can be iffy, and we got back an hour later than we were supposed to on the official excursion.
We did Pisa/Livorno on our own no problem but did not regret doing the official Rome excursion.

Because these are regional trains, you don't have to worry about them selling out. You may or may not get a seat, but you'll be able to get on the train.

Thank you everyone for your input on this subject. I will definitely check out the cruise timetable, thank you for that! Yes, it would be expensive to catch up to the ship, but it leaves at 9 pm. and out tour ends at 3:30, so I think we can make it, and yes as a last resort, taking a taxi (we are 5 people) is an option.
Kaypea