If you're looking for anime similar to Eve: Demon Dance Tokyo, you might like these titles.
Kuraki has taken his grandfather’s ancient sword to the Shinnagi festival for an ancient cleansing ritual, and finds himself inexplicably drawn to a beautiful shrine maiden. As night falls, the priestess is revealed to be Nanachi, the son of the guesthouse Kuraki is staying in. The bond between the two is strengthened as they discover they share the ability to see spirits and use the ancient Japanese magic of Izumo. However, on the night of Nanachi’s initiation as a shaman, Kuraki accidentally sees a ritual sacrifice that is an attempt to break the curse of Susanoo, and becomes the target of the newly instituted and blood-thirsty leader...
"Episode 13.5" is set between episodes 13 and 14, and depicts the shocking incident that occurs during Celty and Shinra's romantic trip together.
One day, when they were children, Maya and Ami were out playing in the summer sun and happened upon a mysterious and legendary creature known as a Tsuchinoko. Lovingly naming it Tsucchi, the pair decides to keep it as a pet. Now the two girls must train themselves to avoid Tsucchi’s attacks, try to find out what it likes to eat, and attempt to find a partner for their beloved new pet.