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. Sapphire is the birthstone of September, and pink sapphire is a very popular gemstone in jewelry today. The bright and happy color of a pink sapphire ring is both playful and trendy.