Syros and Amorgos are two very different ideas of the Cyclades. Syros is the islands' capital, a working town of marble squares, grand mansions and a harbour that stays busy all year. Amorgos is the long, steep island at the south-eastern edge of the group, known for its cliff-hung monastery of Hozoviotissa, its walking paths and its deep blue water. Travellers pair them when they want a city break and a wild island in the same trip.
The direct connection is thin, and knowing that early will save you a lot of re-planning. Blue Star Ferries is the only company on it. According to Ferryhopper, its ships reach Katapola, the main port, on 2 to 3 days a week, and Aegiali, the northern port, once a week. The trip is long for the distance, 5 hr 5 min at best and 6 hr 5 min on most sailings to Katapola, because a conventional ship on a multi-island run spends time at other ports along the way.
The biggest catch is summer. Ferryhopper's monthly table, which is based on last year's sailings, has sailings from Syros to Amorgos in every month except July and August, when it shows no data at all. If you are travelling in high season, expect to change boats, usually on Naxos or Paros, both of which have summer sailings from Syros and on to Amorgos.
Before you book, decide which Amorgos port suits you. Katapola is best for Chora, the monastery and the south of the island; Aegiali suits stays in the northern villages and the beach there. The two are a long drive apart, so the port on your ticket matters as much as the date.