Karasu wa Aruji wo Erabanai

Historical East Asia, royalty, political tension, conspiracy, mystery and murder in the palace, all of this and more found in Yatagarasu and The Apothecary Diaries 

These series both take place in a palace setting and have a similar vibe. Mystery and secrets are important to the plots of both stories, and the protagonists of both series are somewhat forced into their roles initially.  

Both anime have historical settings with main characters getting roped into events by powerful people in their country. While Apothecary Diaries focuses more on it's medical, mystery, and comedy aspects. The Raven Does Not Choose It's Master focuses more on it's political events, story, plot and world building. Both have some similarities in their qualities and are very good in their own right and whichever one you'll prefer depends on which of it's main aspects suit your tastes better. Overall you're likely to enjoy both of them if you liked one. 

Setting of ancient feudal china with royalty or royal family as one of the main focus. Also the servent lord relationship is similar. Both have a mysterious vibe. 

It's hard to find anime that really throws itself into a court setting (at least compared to Chinese+Korean media), and the only two off the top of my head are these. The main difference would be the realms they take place in- Koukyuu no Karasu is fully within the human realm, but is innately supernatural through the involvement of the protagonist. The Raven Consort! Mystery, suspense, some gore, and beautiful court costumes. Ravens. Consorts, even.