What prayer is said when extinguishing the yahrzeit candle?

No prayer is required when extinguishing a Yahrtzeit candle, because according to tradition, a Yahrtzeit candle is not to be extinguished. It should be let burn for the entire 24 hours of the anniversary, beginning at sundown. If the candle must be extinguised because of a safety issue, it may be extinguished without a prayer. If at all possible, however, you should arrange to be around long enough to allow it to burn out naturally.

If this is impossible for you, there are alternatives such as electric candles which may be safely left on for 24 hours. There is nothing special about the candle itself, and any candle or light source that can remain lit for the full 24 hours may be utilized. The same light should not, however, then be used for other purposes.