A traditional gift for an anniversary, these Sapphire rings are also appropriate for any occasion at all. 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. 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.