 If you liked
Kamichu!
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 ...then you might like
Natsume Yuujinchou
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Natsume Yuujinchou and Kamichu are both somewhat slice of life series which revolve around a young person with supernatural powers. And, of course, both series feature an awesome cat!
Both have the same slow pace, and the protagonists can see those kind of "ghosts" or fantastic creatures.
Stories where humans and the supernatural mingle together.
Kamichu is a very lighthearted look of this delicate and strange relationship, somewhat reminiscing My Neighbor Totoro by Studio Ghibli.
Natsume Yuujinchou takes a deeper and a quite more painful look into this relationship, introducing us to a string of beautiful stories between humans and youkai that are touching and often times sad.
Both are set in the summer, a time of the year that fits both series perfectly.
A slice of life where there is interaction with shintoist figures. Kamichu has more gods than anything while Natsume Yuujinchou has youkai.
It has the same heartwarming and yet melancholy tone. The main characters can both see gods and supernatural beings and possess of supernatural powers, without being flashy about them. Friendship, getting along, solving problems and helping both people and creatures seem to be an important theme in both.
The Japanese gods and creatures are also the same.
Other recs I can think of are Spirited Away and XXXHolic