Trains from Rome to Civitavecchia Cruise Port, and from cruise port to Fiumicino airport

You can check schedules at www.trenitalia.com/tcom-en. It would help if you mentioned where in Rome you'll be staying prior to the cruise, as Roma Termini may not be the most convenient departure station. For example, the Trastevere or San Pietro station may be closer to your lodgings, and the trains departing from Roma Termini pass these stations on their way to Civitavecchia.

We have done it a half dozen times. Depending on time of day, day of week there are at two or three trains an hour from Rome Termini to Civit.... taking roughly an hour. Some a little quicker and some a little slower. It is basically a commuter run between the two points. It is a half miles or so walk along the beach to the cruise port. There is a city bus that runs that route and taxis available if you don't want to walk. There is no train between Civit.. and the airport. You have to connect through Rome to get a train to the airport. There is a little short cut by taking a train to the St Pietro stop and then the train to the airport. Or go all the way into Termini and take the Leonard Express to the airport. Under the best of conditions I would allow at least three hours to do that. If I knew you exact schedule it would be easier to recommend a specific route.

If you have a return flight the day you departure the ship, I would consider taking the cruise line shuttle to the airport. It is expensive. If I remember correctly it could have been a hundred US dollars/person for the shuttle so you are really paying for the door to door convenience. But sometimes it is worth it. Since the airport and Civit.... are somewhat on the same side of Rome, the shuttle is only an hour or so to the airport.