Meeting royalty can be intimidating and uncomfortable. Get familiarised with the protocol for meeting royalty from different parts of the world, and your royal encounter is sure to go smoothly.
When meeting European royals, especially English royals, don't speak unless spoken to, use the official formal address and from then on in the encounter use "sir" or "ma'am." Men may bow their heads. Women may curtsy. Don't extend your hand for a handshake until the royal does first. Briefly and gently shake the royal's hand.
In Asia, each royal family has its own protocol, so research the culture in question. When meeting Japanese royals, follow the protocol for meeting Europeans. Thai royalty, however, must not be touched or spoken to.
The Middle East
While protocol for meeting Middle Eastern royals is similar to protocol for meeting Europeans, Middle Eastern royals are very unforgiving about certain offences. Don't make extended eye contact with the opposite sex in general. Men, don't look women in the eyes or extend your hands first when meeting women. Wear modest clothing that covers your arms and legs. Women, wear head scarves.