I think this is what you are after: http://www.snav.it/en/destinations/sicily.html
The SNAV overnight ferry from Naples to Palermo will be cheaper: 50 Euros (all-inclusive) for a reclining seat (1 passenger); 140 Euros (all--inclusive) for a twin inside cabin (2 passengers). This ferry has the advantage of running DAILY.
If you're staying along the Amalfi Coast, you can take the SITA bus from Amalfi, Atrani, Minori, Maiori, Erchie, Cetara or Vietri sul Mare DIRECT to the Naples Port (3.40 Euros) in time to board the overnight ferry to Palermo at 20:00.
http://www.sitabus.it over 7 years ago