Here is a recap of transportation options for travel between the Bay of Naples/Salerno and Sicily:
Overnight ferry Naples/Palermo:
Overnight ferry Naples/Catania:
Overnight or daylight ferry Salerno/Messina:
Overnight or daylight ferry Salerno/Palermo:
Overnight or daylight trains:
Airlines:
www.alitalia.it (Naples/Palermo; Naples/Catania, all using Air One aircraft)
www.airitaly.it (Naples/Catania)