The Ancient Magus' Bride - Videos

Both shows feature magic and magical beings, pastoral European settings, and the stories include solving problems that revolve around magic. Both have some romantic tension between the lead characters.

Magic, fairies, and wondrous beings. Plus, a sweet tinge of romance, let's not forget romance.

Both have girl characters with red hair and take place in England. Both take place in a world where magic is not really seen by most people any more. Both series have the young girl helping a male character through an incredible journey while learning about themselves. 

they are very similar in :

both of them about a human and supernatural being

 both stories about helping other supernatural beings 

both of the main characters have a similar childhood and growup in a similar way 

both of the characters found a supernatural being that give them home and a peace 

The Ancient Magus Bride and Natsume's Book of Friends both have a "normal" human protagonist with a certain special power that ends up in situations that involve magical creatures, that they help or have to survive encountering. They're both very touching.

The main character in both these stories has been misunderstood, neglected and somewhat abandoned by society at a young age for being able to see (and get attacked by) supernatural beings. In both, the story begins at a point where they've been taken in by someone who will care for them, so the focus is on how they gradually heal and learn to open up to others. Natsume Yuujinchou is more gentle and sometimes bittersweet, while Mahoutsukai no Yome is a bit more violent and dark, but has an ethereal otherworldly atmosphere to it.

Both female main characters love books, surrounded by characters who each have their own set of issues from the past, they both give off a similar FEEL, if you enjoy one you'll more than likely enjoy the other.