Gakkou no Kaidan, Natsume Yuujinchou Recommendations
The lead characters have inherited a book that belonged to their deceased mother/grandmother and that it has something to do with ghosts, spirits and the like. :)
The protagonist in these both find a book that was used to seal demons. The monsters are based on Japanese ghost stories.
In Natsume Yuujinchou, the main plot was to release captured demons. In Ghost Stories the protagonist accidentally releases all the demons sealed in the book, and needs to find and reseal all of them instead. Both the mascot characters that help the protagonist is a demon in the shape of a cat.
Extremely similar stories~ almost annoyingly similar. Both protagonists have inherited a book containing the names of the youkai their grandmother/mother fought, with the slight difference that in Natsume Yuujinchou, the boy wants to release those youkai, whereas in Ghost Stories, the girl releases them by mistake and tries to seal them again.
They are both helped by strong demons which get by in a cat form, called Madara in Natsume Yuujinchou and Amanojaku in Ghost Stories.