Early American ambassadors to the United Kingdom and France set the precedent for US citizens, who need not bow to royalty. However, Americans do follow the established protocol for meeting the Queen or any other member of the Royal Family:
1) Wait for the Royal to speak first.
2) Wait for the Royal to extend his or her hand. If a woman greeting the Queen chooses to wear gloves, which need not be white, she shouldn't remove them before meeting Her Majesty.
3) Women need not wear hats before 6:30 p.m.
4) Call the Royal by his or her appropriate title, using a more formal title, such as "Your Majesty" for the Queen and "Your Royal Highness" for the Duke of Edinburgh on first meeting and there after (if the conversation continues) "Ma'am" or "Sir".
5) Stand when a Royal enters a room.
6) Don't turn one's back on the Royal.
These manners aren't too difficult for most Americans to handle. Most Southerners, such as myself, for example, call anyone older than themselves "sir" or "ma'am"; men seated at a table in a restaurant rise if a woman comes over to their table as do women when greeting an older person. Both Houses of Congress rise when the President enters the House Chamber to address the joint session.
Finally, I'd like to retire the stereotype that all Americans are boorish clods. Benjamin Franklin charmed Georgian England, and Thomas Jefferson achieved rock star-status at the Court of Versailles, so we have a long tradition of gallantry to uphold. I'd also hope that Americans extend similar courtesies to everyone they meet abroad since we are all roving ambassadors.
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