Here's why:
* Shrunken Girl: The main female character, Louise Françoise le Blanc de La Vallière, is a poor magic student at a prestigious academy. She is known as the "Zero" due to her inability to perform magic. During a summoning ritual, she accidentally summons a young boy, Saito Hiraga, from Japan.
* Young Boy Caregiver: Saito is initially bewildered and is treated like a slave by Louise, who is the "familiar" he is bound to. As the series progresses, they form a strong bond, and Saito becomes her protector and trusted companion.
While not a shrunken girl exactly, the "familiar" aspect of the story creates a dynamic where Louise, despite being a powerful noble, is reliant on the small, seemingly ordinary Saito for protection and support.
There are other anime that might fit your description, but "The Familiar of Zero" is the most prominent one.