Akagami no Shirayuki-hime, Mahoutsukai no Yome Recommendations
Both are about red-haired girls finding their place in society, with one being a mage and the other being a court herbalist. While their personalities certainly differ, both girls eventually become driven at being the best of their kind. I enjoyed the fantasy setting and the development of romance equally, though Shirayuki-hime definitely is more romance-driven while Mahoutsukai focuses more on the lore and worldbuilding.
Both have similarly relaxing atmospheres and a red-haired heroine that is whisked away into a new life. While Shirayuki is centered around court life, Mahoutsukai has more fantasy elements to it. The romance element is there in both, but Mahoutsukai's romance is not as intense as Shirayuki. If you enjoy a gentle story, fantasy or other-worldly, and beautiful and soft animation, then you will enjoy both of these shows.
Both have a character and a troubled past. They are also male protagonist with Influence/Power to protect them.
However, unlike Shirayuki-hime, Mahoutsukai does not focus on much romance. But they are still very similar.
-Both protagonists are apparently similar (short red hair, green eyes), in addition, they also have a slightly shy personality. This, I believe, should be the main similarity between both animes;
-Romance with a important characters that happens to treat the protagonist well;
-Both have similar environments, in a place close to nature.