Or at least the two he's currently taking on the road with him.
These are both made by Stefan Sobell. The older of the two is a Martin Simpson signature model. This has Brazilian rosewood back and sides and a European spruce top. This is the guitar facing you in this photo.
This was the one he used for his slide work. It's strong with 80:20 mediums, but the two plain strings are from a heavy set (the 1st is a 0.015!). He played a couple of finger style pieces sans slide on this one as well.
The guitar with it's back to you there is a Sobell "New World" model. Adirondack spruce and african blackwood. Strung with mediums. Here's the front of that guitar. The bridge is asymetrical.
Martin Simpson uses a Highlander UST on both these guitars. The output from the pickups goes into a Fishman pre-amp.
The Sobell guitars look pretty interesting. Both these guitars had cuved back and tops. I say "curved" because the curvature is not as extreme as on an arched top guitar, but certainly the tops aren't flat.
Sobell also makes an interesting "D" guitar. This is a bit like a guitar with 12 frets to the neck. The reason these guitars often sound different to the equivalent 14-fretter is that the bridge is moved back towards the heel, so there's more wood between the sound hole and the bridge, and less between the heel and the bridge. What Stobell has done is to stick with that bridge posititioning but add two frets back. You end up with a long-scale guitar and the idea is that it's tuned down a whole tone (IE capo it at the 2nd fret and you're in standard tuning).
Links to details on these Stefan Sobell models....
The New World
Martin Simpson signature
Sobell "D"
