Rome is not itself a cruise port, but is served by the port of Civitavecchia. In total, Civitavecchia is the eighth busiest cruise port in the world, departure point of around three hundred sailings yearly from Norwegian, Celebrity, MSC and more to the Mediterranean and Europe, along with other places.
Sailings departing from Rome during the the peak season of summer are considerably more expensive than the the low season of winter. Overall cruises from Rome are somewhat affordable compared to other ports. The illustration below shows the monthly average cost per day for cruises from Rome.
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