Speaking as a theorist here: while there are automatic chord analysis functions in many notation programs, in my experience, they are all not yet sufficiently aware of context (upon which a harmonic analysis is heavily dependent) and analysis style. It's quite easy to label chords as to the pure vertical content, but such labeling is going to be meaningless without the context. Others have gone into the problem of assuming enharmonic equivalence and labeling <G C E> as Em#5, so I won't, but I'll add that if the G is the bottom note, then in much of the music I deal with, you can safely assume that the C and E do not have harmonic function and are ornamental notes, or that the entire simultaneity is of a decorative rather than functional nature. Explaining functional harmony to a computer is a bit more difficult than labeling the content of a simultaneity. There are various approaches in computational musicology, and I'd be happy to find some links if people are sufficiently interested.
As for the 15th century, while chordal analysis in the post-Rameau, functional sense is a bit silly, there's quite a lot of mileage to be found in examining successions of simultaneities. It's my special field, as a matter of fact...the usual software to help with analysis of this sort is Humdrum or music21. I don't know how many of the other people involved with those are in this group, but since a bunch of them use LilyPond, they may yet wander into this thread!