Amorgos is the long, steep island at the eastern edge of the Cyclades, loved for its cliff-top Chora, its walking paths and its clear, deep water. After Santorini it feels calm and unpolished, with fewer day-trippers and a slower rhythm, and it is a natural next stop before heading on to the Small Cyclades or Naxos.
The direct link between the two islands is seasonal and depends heavily on one company. Seajets runs a high-speed boat that covers the 43 nautical miles in about 1 hr 15 min, sailing anywhere from once a week to every day depending on the month. Beyond that, the options thin out: the small Express Skopelitis of Small Cyclades Lines sails once a week in some months and takes around five hours because it calls at Ios, and a Blue Star Ferries sailing showed up only once a week in one month of last year's data.
That leaves a big price gap. The fast boat started at €77.70 when we checked, while the slow conventional sailings started at €11.50. If the cheap boat runs on your day and you have time, it is a bargain; most travellers, though, will be on Seajets.
All direct boats arrive at Katapola, the main port in the south of Amorgos, not at Aegiali in the north, so if you are staying in Aegiali, allow for the drive across the island. And because there is nothing direct from November to January, winter travellers need to go via Naxos or Piraeus.