The Meisel COM-90
does it, no sweat.
The sensor for the tuner is in the clip
, which contacts the surface of the instrument. I believe that this makes for better pickup of the instrument (most tuners with the swivel clip have the tuning sensor in the head of the tuner - if you can swivel it in endless circles, you know that's the case).
See the video below; I just (sloppily) filmed the tuner on a bass with the E-string tuned down and it picks it up well. With the fuller, better fundamental on a real
B-string, I can only imagine it should be even better. Full disclosure - we sell this tuner at our store.
But you can get it at several retailers other than us as well. Video of tuner in action: http://www.youtube.com/watch?v=6QiC4FyKBcM