Blue Topaz engagement rings? Absolutely! Diamonds may be a girl's best friend, but Blue Topaz engagement rings are a unique, original, and a far more affordable choice. The birthstone of December, the tranquil azure color of a blue topaz ring can evoke thoughts of warm Caribbean seas on a cold winter day. The birthstone of December, the tranquil azure color of a blue topaz ring can evoke thoughts of warm Caribbean seas on a cold winter day. 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.