 If you liked
Cardcaptor Sakura
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 ...then you might like
Natsume Yuujinchou
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Both have a animal-like sidekick and are mostly about capturing things like animals and ghosts.
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Recommended by DragonsWhip
Both are shoujo that have a procedual monster of the week kind of premise to it and both leads have a cute animal sidekick to help them along the way as well too.
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Recommended by Disapeared_Ghost
Both include supernatural beings and magic. Both have protagonists with admirable qualities. Both protagonists are guided by a strong entity trapped inside an inferior form.
Both are very relaxing and touching. Both are episodic in nature.
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Recommended by HanezeveAbyss
Both are light but emotional shows with a very kind/wholesome protagonist that has special powers but cannot reveal it to most of their friends and family. They deal with problems related to supernatural creatures in an episodic manner. Both have a supernatural Kansai dialect-speaking animal-looking sidekicks that is gluttonous and comedic, but can transform into a more imposing and powerful form that talks with a more serious voice.