Sora wo Miageru Shoujo no Hitomi ni Utsuru Sekai

Two worlds that somehow exist in parallel universes one of which is somewhere in the sky (or even space), a plain girl who has some powers to influence the fate of the world. Surely, Escaflowne is far more better in all aspects but Munto is the closest to it in the idea itself and plot. 

girl seeing another parallel world because of her dormant powers. She helps the King from that parallel world by lending her powers. The story is very similar to the Vision of Escaflowne. 

Both animes involve a female from earth having a unique power that is needed to help a king in another dimension (mirror of earth) - in order to save it. Escaflowne has more romance involved in the plot and is longer in length then Munto. If you like one, you will like the other.  

What struck me about Munto is how extremely similar it is to Noein. A young girl is sought out by people from another time and space because she has an important power that will save their world from destruction. The fact that the opening artists are the same is just an eery start, the characters, concept, mood, art style, animation, the setting, etc. all share lots of parallels with eachother. Obviously there are key differences between the two series, but it's definitely worth checking out the other if you enjoyed either of these series. 

Both male / female characters have many similarities. Noein is longer then Munto, and a but darker. If you liked one, you will like the other.