If you can spare three or four days you’ll add the Pantheon, Trastevere and slower meals without a checklist feel, then travel out to the port on sailing day (about an hour by train or transfer).
Don’t cut it fine
Book your Rome stay to end on embarkation day, not the night before, an extra night in the city is far cheaper than missing the ship if a flight is late.
Three ways we’d do it
Fly-cruise · 10–16 days
Barcelona + Mediterranean Cruise
Fly to Barcelona, settle in for two nights, then sail the western Med.
Barcelona → Naples → Civitavecchia → Rome
Rail journey · 12–16 days
Italy Without Flying
Milan → Florence → Rome → Naples, all by fast train.
Milan → Florence → Rome → Naples