Akuyaku Reijou no Nariagari ~Ringoku de Houseki no Seijo to Yobareru Made~

Our protagonist is the daughter of a duke and is someone who gets lost in her own world when it comes to gemstones, Lady Eliza. While being crowned at the wedding ceremony with her adulterous fiancé, Prince Makis, she is able to correctly identify the nationally treasured tiara as being counterfeit. By revealing this, and calling it trash, Prince Makis breaks off the engagement right then and there and exiles her from the country. She's then welcomed by a neighbouring country's crown prince and begins her exiled new life there...