Soap and Water
It is the easiest way to clean your sapphire ring. Take some liquid soap and make a solution with water. Dip the ring in the solution and leave it there for about 20 minutes so that the dirt stuck in it can soften. Wipe off the debris with the help of a soft cloth dipped in the same soap solution. Whatever debris is left can be removed with the help of a toothbrush. Once you are done, clean it gently with a soft cloth. It should be very clean.
Ammonia and Water
This is a slightly radical approach but it works well. Take normal household ammonia and add it to water to make a 50% concentration solution. The solution is known to leave the sapphire shiny. Once you make the solution, leave the ring in it for about 10 to 20 minutes. Afterwards, rub it with a toothbrush or a cloth to get rid of any impurities that may be in the ring. After you are done, rinse it with water making sure that there is no residue of the solution left in the grooves of the ring. Clean it with a towel. It should be sparkling.
Ultrasonic Cleaning Machine
These should only be used with strong stones such as the sapphire. Softer stones should be cleaned with more traditional methods as a precaution. To add some shine, a few drops of ammonia can also be added to the ring prior to the treatment. Once the process is complete your sapphire ring should look great.