Maid to Maze ~Anata no Soba ni~

This country is full of dungeons. Main character is a prince how is suddenly announced that in a year he will need to inherit this kingdom. In order to gain public support he sets off to exploring a dungeon, but appears to be too weak for the task. In order not to look weak he asks a maid who is superior to warriors to accompany him on this task as a bride candidate.

[From vndbreview]