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Did you T/A book the cruise and the flights with Celebrity? If so then you are covered and the ship will wait for you. If your T/A booked the flights independently then it is your responsibility to get there on tim.
If you book a "package" of cruise + flights with a cruise line through a travel agent then the cruise line is responsible for sorting you out with any delays. usually the ship will wait if there a large numbers on one flight. If however, you have booked a "cruise only" and booked separate flights, then the ship will not wait for you and you are on your own. Most cruiselines organise flights as part of the package, often using scheduled flights.
I can understand that it might seem a worrying situation but most cruises out of Civitavecchia (Rome) are serviced by flights which arrive that day and if it is arranged with Celebrity they will have contingency plans for delays. As it is that far in advance you might consider an add-on through Celebrity at an hotel in Rome but I will warn you that Rome in August is extremely hot and is probably not worth the trouble. I would think that your flight will be an early one 7/8ish arriving in Rome 10/11ish, you lose an hour because of time difference, which will give you an overlap of about 6 hours. Just to recap...your schedule is normal and happens that way all the time for cruises out of Rome .... regards ..... Nei.