Genmu Senki Leda, Tobira wo Akete Recommendations
In both anime the heroine gets transported in another world where she finds out that she is a legendary warrior and that she must fight against an evil ruler.
In Tobira o Akete the main heroine discovers supernatural powers before coming to another world, in Genmu Senki Leda she discovers her powers in the other world. The "other world" itself is different in both of them, but the idea of saving strange new world is the same. Both have a romantic relationship, superpower and fights.