White Topaz engagement rings? Absolutely! Diamonds may be a girl's best friend, but White Topaz engagement rings are a unique, original, and a far more affordable choice. A sparkling white topaz ring is just the thing if you like diamond jewelry but you're on a budget. We won't tell if you won't! 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.