Several of the bands previously mentioned (Early Music Consort (?), Baltimore Consort, Dufay Collective) use period instruments when performing "period" music. We should also remember what certain wits have pointed out: It was not the intention of the composers of the 14th century that their music should be performed only in accordance with their intentions!

I recently did a 14th century tune on a mountain dulcimer, a 19th century instrument with roots which can be documented to no earlier than circa 1550 in western Europe. Though I say it myself, I thought the music and the the instrument were a good match.