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Choose sodium-free club soda or seltzer water as salt may damage the jewelry. The carbonation in the soda or seltzer helps dislodge grime from the necklace. Put a few drops of any mild dish soap (free of dyes, perfumes, and moisturizers) in the club soda, then agitate the liquid to mix it up. If you don't have a strainer, you could put the necklace directly in the bowl, though the strainer helps you remove and rinse the necklace. If the strainer is too large to fit in the bowl, reserve it for rinsing the necklace. After 5 minutes, swish the necklace around in the solution to dislodge grime. Then, use a new, soft toothbrush to clean the chain, settings, crevices, gemstones, or charms. Scrub in a gentle, circular motion applying a minimal amount of pressure. Use warm, running water to rinse the club soda, soap, and debris off the necklace. The strainer is helpful for this step, as you can let water run over the necklace and through the strainer. Choose a soft, lint-free cloth to pat the necklace dry with, paying special attention to nooks and crannies. Then, lay the necklace out on the cloth to continue drying. A lint-free cloth is necessary to ensure fibers don't become stuck in the crevices or chain. You could use a blow dryer on a warm setting to speed up the process, if desired, or simply let the necklace air dry completely.

Summary:
Add a few drops of dish soap to a bowl of club soda. Put the necklace in a strainer and soak it in the bowl for 5 minutes. Scrub the necklace with a new, soft toothbrush. Rinse the necklace. Dry the necklace with a lint-free cloth.