Trenitalia runs the service, but schedules will update on 10 June, so continue to check for updated schedules.
You haven't indicated your date of travel, but Liberty Lines runs direct hydrofoil service from last June between the Aeolians and Palermo. There's only one daily run, so book online in advance.
VagabondaEdited: 16 May 2018, 08:03
Thank you, Vagabonda. Great help as always. Do you know if train tickets need to be purchased in advance? We are traveling mid-October.