Haikara-san ga Tooru

Both have a reddish haired girl as protagonist, who was engaged to someone without her knowledge. In Haikara, the protagonist moves to the fiance's house and gets to meet his family, in Mikakunin the fiance moves to the protagonist's house, bringing family members with him. In both cases, the protagonist has to deal somehow with the new situation, and gets gradually attached to the fiance. If you are interested in a romcom with an arranged engagement, both titles may be for you. 

Romantic comedies set in Taisho era Japan where the couple is already bound by an arranged marriage at the beginning of the show. There is a wealth-gap between the couple, with the male being from a more aristocratic family. 

These are romances with a female protagonists taking place between the ends of world war 1 and world war 2. One series takes place in Japan mainly, the other in Europe. Haikara san focuses more on comedy, the weaknesses of the protagonist and her development in life and love, while Alpenrose is more about the adventures of the protagonist while chasing her love against external obstacles. However, if you like a romance story in a historical setting, with a protagonist who becomes more and more daring in the pursuit of her goals, both titles may be for you. 

Both titles take place in about the same time frame, during the early 20ties of the 20th century in the Tokyo area I guess. And both feature a clumsy female lead with a hot temper, which can get herself and others into trouble. If you want to see a Romcom/Harem with the same historical background and a moody female lead, both titles may be for you.  

Both series take place during the Taishou era in Japan. And follow young women trying to fight the archaic Japanese role of women being "seen not heard", being a proper wife (cooking and cleaning and other Yamato Nadeshiko ideology), and submitting to the decisions of male figures in their lives. They attempt to do 'boy' things such as practicing kendo in "Haikara-san ga Tooru" and playing baseball in "Taishou Yakyuu Musume." which ultimately are given grief from their teachers and parents. Granted both anime show the girls putting up a good fight but they do quickly submit to the romance and arranged marriages forced upon them as typical of any anime with these tropes. read more 

While ONKT is only a small ova and HSgT a long anime, both feature a heroine that is a lady in Taisho Era and falls in love with someone she is not supposed to. If you enjoy sweet historical shoujo, you might want to try these.