 If you liked
Kyuuketsuhime Miyu (TV)
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 ...then you might like
Kyoukai no Kanata
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Kyoukai no Kanata and Kyuuketsuhime Miyu both have female main characters that kill demons as spirit warriors, male companions that are at least half-demon and interested in the female leads. They are dark fantasies that have the main characters involved in a lot of action and introspection. The personalities of the main characters are very different, but if you like one of these, you should watch the other.