Himiko-den

A high school girl (Himiko/Himeko) is suddenly thrown into an otherworldly situation with her closest friend to fulfil a predetermined destiny under a long-hailed title (Boka/Solar Priestess). Both series have some pretty legendary action scenes, heavy supernatural elements and a ton of drama. They're both 12 episodes as well so good if you're looking for someone shorter; and relatively happy endings. 

Both have female protagonists sent to a medieval-ish looking world to help restore a land that was taken over/ravaged by a neighboring country. The girls have powers and try to help while looking for a way back to their own world. It's very similar, trust me. 

school girl transported to another time in the past that is not found in the history books. epic battles, demons of some what, magical power 

A high school girl with some of her friends transported to another world and later have to deal with problems which exist in that world. They will have a lot of important peoples along side their quest and there is many other similarities which you can see for yourself. Although they tell the story in a different way I think they both are a good watch.