Kenjutsu Komachi summary:

Komachi Mizuno's family runs a shrine and a sword fighting dojo, but she doesn't like fighting and often skips out on practice. On Komachi's 16th birthday, she is mysteriously transported to another world similar to classical Japan. There she learns of a certain God who holds the key for her return. She will learn what she holds dear, but will she be able to complete her mission tin order to return?