If you're looking for anime similar to Chaika: The Coffin Princess, you might like these titles. All recommendations are made by Anime-Planet users like you!
The god Mauser delivered unto a world of magic a prophecy: if the Scrapped Princess is allowed to live, she will destroy the entire world. But the knight who was to kill her could not end the life of a newborn child, and so she lived. Fifteen years later, her adopted brother and sister have sworn to protect her, and together they travel from town to town, searching for a life she can't have.
Both Animes are done by Bones, have similar plotlines, and even similar characters. But the differences make both enjoyable in their own right. Scrapped Princess is a story about a young lady with a dark destiny, something will happen on her 16th birthday and everyone believes that it is a dark destiny (possibly world ending). In contrast, Chaika: Coffen Princess is the story of a young princess who is on a quest to recover her slain fathers remains. For what purpose remains to be seen. Both are compelling stories with well developed characters (that you actually care about). Simply put, if you like one you will like the other.
Both anime are based on light novels written by the same person. Both are fantasy action adventure series and have somewhat similar main character trio. A girl (and a princess in some sort of way) who needs to be protected and siblings who protect her. I think there is really no point mentioning all the similarities, so I might mention a few differences instead. At times Hitsugi no Chaika can be much darker and gorry than Scrapped Princess and last but not least, many characters in Hitsugi no Chaika are named after cars, rather than named after guns like in Scrapped Princess. If you've seen one and liked it, the other one should be right up your allay.
Hitomi was just a normal high school girl, until she was taken by the mysterious Van Fanel and dropped into a world of romance, magic and giant sword-wielding armor suits! Now Van, pilot of the famed armor suit Escaflowne; and Hitomi, whose hobby of predicting the future just became a frightening reality, must work together and fight the advanced technology of Zaibach: a force who want to shape Gaea to their visions of "peace". Follow Hitomi in her struggles against both these forces who seek to conquer this world, and her own confused heart.
Chaika: The Coffin Princess and Escaflowne both have a number of similar elements. Specifically, they both have a setting in which magic and technology are mixed in an interesting way, and are visually inspired by traditional fantasy for the most part. They are both fantasy adventure stories where politics eventually get involved. Escaflowne has a main character who comes from earth, and is thus an effective proxy for the audience, which is something Chaika only sort of has, with a slightly ignorant main character, so if the main reason you loved Escaflowne was that it featured a shcool girl trapped in another world, then maybe this is not a perfect recommendation. I am sure most people would enjoy both, though.