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. One of the oldest gemstones in history, garnet is the birthstone of January. Garnet rings have been popular since Victorian times, and are treasured for their deep red color.