Amethyst engagement rings? Absolutely! Diamonds may be a girl's best friend, but Amethyst engagement rings are a unique, original, and a far more affordable choice. As the gem of peace and tranquility, amethyst is mesmerizingly beautiful. A durable and affordable gem, an amethyst ring is excellent for every day wear. Sapphire is the birthstone of September, and one of the most popular gemstones on the jewelry scene today. The deep blue color of a sapphire ring is just right for an evening out.