I couldn’t recommend the Whiskey Bards enough. “Come Walk With Us” from the first album makes me want to grab a sword and head off to war. And a great bunch of guys to boot. 
Loreena McKennitt has the right kind of feel for what you’re looking for. Mostly not historically accurate, but evocative of the time period you’re interested in. While some of her music has a Celtic feel, she also mixes in lots of other influences. She makes use of exotic and historic instruments like tamboura, dulcimer, harp, and hurdy gurdy (funny-sounding name, but I swear that’s what it’s called).
Earlier Sarah McLachlan has a much more folksy feel than Fumbling Towards Ecstasy and after. You might like Solace and Touch.
I’ve heard that Lisa Gerrard’s work after she left Dead Can Dance also has a medieval feel, but I haven’t actually listened to any of it.
Also, if you’re looking for purely instrumental, check out English Renaissance Music by Canadian Brass. I’ve got it, and always enjoy listening to it.
Sting’s new album, Songs from the Labyrinth , is actually very good - Lute songs (almost all Dowland) from the Elizabethan period.
Richard Searles does a lot of instrumental Renaissance- and some Medieval-era music. I’ve got this album from him. Nice, mellow, proficient, odd and archaic instruments galore.
I like the Mediaeval Baebes too. Have their first disc from about ten years ago. And yes, they are total baebes, but they can sing too.