Folegandros and Amorgos are two of the Cyclades' most admired quieter islands, and they sit far apart: Folegandros in the south-west, near Milos and Sikinos, Amorgos out on the eastern edge beyond Naxos. Leaving the cliff-top Chora of Folegandros for the hiking paths and long coastline of Amorgos makes a striking change of scene, and a direct boat saves you a day of changing ships.
That direct boat is a single Seajets catamaran, and its timetable is patchy. Ferryhopper lists the route from April to October, but in last year's monthly figures for this direction, sailings appeared only in April (once a week), May (6 days a week), September (3 days a week) and October (every day), with no data for June, July and August. Do not assume there is a boat in high summer until you have searched your dates.
It is a quick trip for the distance, about 2 hr 25 min over roughly 75 nautical miles, but not a cheap one: €96.70 per adult when we checked, and €193.39 for two. The catamaran has no car deck, so if you are driving, you will need to route through another island on a conventional ferry.
If the direct boat does not run on your day, Santorini, Naxos, Ios and Paros all have boats to both islands, which turns this into a two-leg trip. It takes longer, but the conventional ships on those legs usually cost far less. Whichever way you go, book the Amorgos port that suits your stay; the direct boat uses Katapola.