Hi Jean, there are a few ships which do that, such as
Seabourn Spirit on June 6 (Rome to Venice), returning same route June 20 - not sure where it goes between, but both of these are 7 nights.
Repeated in July,
Crystal Serenity and Windstar Winsurf both June 14 (Venice to Rome),
Windstar has some hot prices for the ship rating, but entertainment is VERY limited. They reverse the journey 26 July.
Silversea Whisper 27 June (Rome to Venice), returning 1st August.
Silver Wind joins in 7th August (R to V)
and so on, however I didn't see any of the megaliners listed, but then only looked for a 3 month window.
If you can access the following UK website
You can put in the dates you are interested in, along with the cruise length, and location (Mediterranean). This will list several pages of options, and then search for Venice or Rome (they seem to list Rome rather than Civitavecchia) & see what takes your fancy. But those Windstar prices look great, and must be available worldwide.
Once you have the list, if you click on the ship, you will get a report on the ship size, rating, facilities etc.
Hope this helps, have a great time,
Alan & Katrina