Cleaning Emerald and Diamond Jewelry?

I know that diamonds are cleaned differently then emeralds, the later being a porous stone. How do I clean emerald and diamond jewelry?

Diamonds:
Diamonds alone can be cleaned with any cleaner.

Emeralds:
Avoid sudden temperature changes, chemicals and ultrasonic. A litte soap and water works beautifully.

Stone Emerald Diamond
Stone Emerald Diamond
Stone Emerald Diamond