 If you liked
Akagami no Shirayuki-hime
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 ...then you might like
Mahoutsukai no Yome
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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.
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Recommended by jinneverland
These are great anime to watch when you are feeling down, they pace gently through interesting worlds with soft characters and interesting enough storylines.
Very similar main characters.
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Recommended by okamikotori
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.
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Recommended by Vinagrette
if you like complex romance, maybe I can recommend these two anime for you, both of these anime have a red-haired MC (girl) and have the same nature even though in terms of story a little deviated but in terms of romance it may be almost the same.
-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.
The main protagonists are very similar. Mahoutsukai no Yome (The Ancient Magus Bride) contains a lot more violence/gore compared to Akagami no Shirayuki-hime (Snow White with the Red Hair). There is some romance in The Ancient Magus Bride, but very little compared to Snow White with the Red Hair. Both quite good.
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Recommended by Crypt1dCat
Both series are about red haired and green eyed female protagonists who fall in love and live in a fantasy world. The worlds are beautifully designed and the stories are wonderful. The storyline itself is relaxed and the decisions made by both characters are easy to follow.
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Recommended by Wildfangtanz