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Womance is the word you are looking for.
There is allegedly homance but I have never heard it in use.
"A womance is a close but non-sexual relationship between two (or more) women, a form of homosocial intimacy. The word is the female equivalent of a bromance, being a portmanteau of the words woman and romance."
Someone had already suggested girlcrush: feelings of admiration and adoration which a straight girl has for another girl, without wanting to bang said girl. a nonsexual attraction, usually based on veneration at some level.
UrbanDictionary defines girlcrush as: