I’m pretty sure that you need to first head to Lisbon. I’ve checked a few coach lines that I know of and none of them have direct lines from Sintra to Coimbra. Anyway, once you get to Estacao do Oriente (train station in Lisbon) you can catch the high speed service from Lisbon to Porto that stops in Coimbra.
By the way, Coimbra is a very nice town with a very academic culture!
Hugo about 8 years ago