Several of the big craft brewers from MA represented in tap rooms at Logan. Harpoon, Boston Beer Works and Cisco at least.
Depends on the terminal ... unlike many international airports once you pass security at Logan you are stuck in that terminal.
I think the harpoon tap room is in the delta terminal - terminal a maybe - and beer works is in the JetBlue terminal. Some other spots have craft handles as of my recent travels, but pickings can be slim.
This article might help you figure out your options - http://boston.eater.com/2014/11/20/7254625/where-to-eat-at-boston-logan-international-airport-bos BTW - I've noticed recently that Vino Volo (Terminal E and Terminal A) has started offering some craft beer options in bottles - Jacks Abby, Portico, etc.
I flew out Jet Blue to Sint Maarten last weekend and my wife, baby, and I met up with friends at Beer Works. The IPA tasted great leading into the land of Presidente and Carib...which I enjoyed all week
I usually go to Legal when flying out of Terminal C. They typically have a few options including Wormtown.