I honestly can’t say these books are accurate, but I can say that they feel accurate. Few glaring anachronisms, for example.
Death Comes as Epiphany, by Sharan Newman. About a novice who gets caught up in medieval French politics when she goes to the convent founded by Peter Abelard. Abelard and Heloise are both handled in believable ways, though I don’t know enough of the period to say if they are 100% accurate. This is the first in a series. I’ve only read this one. Much more charming than you might expect.
“Dame Frevisse” mysteries by Margaret Frazer. Dame Frevisse is a nun in medieval England. These books are fascinating, with enough detail about life in medieval times to be really neat. Dryer than the Newman books, though.
Candace Robb’s “Owen Archer” mysteries. I seem to be establishing a theme, here. Medieval England, Archer is Welsh. I’ve only read one (A Spy for the Redeemer) but was impressed by the complexity of the story. A Spy is late in the series, so I was very confused at times. I’d strongly recommend starting at the beginning. Archer does encounter some real historical figures, but none who are famous enough that you’d probably find anything wrong in their portrayal.
Sally Wright’s “Ben Reese” mysteries. Not so far in the past, but so darned good. These are set in the 60’s and Wright is definitely channeling Dorothy L. Sayers. Excellent books.
I love Elizabeth Peters, so I enjoy her “Amelia Peabody” series, but I don’t think I’d ever claim they are historically accurate. Peters is a real Egyptologist, though.
Speaking of Egypt, PC Doherty has a series set in ancient Egypt with a sleuth called Amerotke who is, if I remember correctly, a judge. I thought the story was interesting but, again if I remember correctly, the writing was a bit dull. Like so many people, I find Egypt fascinating, so a good series set there/then would be lovely.
Hope this helps.