With a 12:45 arrival in Athens and a 4:00 departure to Santorini you should have no problem making the flight, even if your inbound is an hour or so late. Again, my apologies for the confusion re Naxos, but there are some comments in that post about passport control, boarding passes & luggage that apply equally to Santorini.

If you are coming from outside Schengen and have to go through passport control it is usually fairly quick in my experience. Customs is simply "walk through the green exit" unless you have something to declare — I've never seen anyone stopped. The Athens Airport terminal is small by international standards, and very efficient. When you collect your luggage walk down the hall a few steps and take the escalator up one level to Departures. This will take about 5 minutes unless you stop to use one of the ATMS. After check-in you should have plenty of time for lunch and a look around the shops.

Thanks. I've just done battle with the Aegean Airlines site only to have it crash just after I put in my bank details and hit "buy". I'll have to wait until my bank account updates to see if it actually went through. RATS. Thanks for the info on Athens airport, I had no idea of its size or how rigorous their restrictions were.

There is a wealth of information about Athens Airport on their website, http://www.aia.gr