Attire also plays an important part in royal visits. The first lady skipped a sleeveless dress -- as is her usual style -- and opted instead for a black sweater, and a black skirt topped with a white shirt, which she accessorized with a pearl necklace, a rather conservative look for a first lady who likes to show off her toned arms.
The president, who is known for his laid-back demeanor, may have had to adopt a more formal tone to discuss world affairs with the queen.
"Whatever you do, don't call them nicknames," Kelly said, or ask about her famous grandchildren, Prince Harry and Prince William.
It's OK to make eye contact and to appear lighthearted -- another plus for the president who made the queen laugh as he told her about his busy schedule and lack of sleep.
When it comes to eating, chowing down was not on the menu. Tea is usually accompanied by small snacks, and protocol dictates that the queen's guests stop eating after she takes her last bite.
General tea etiquette dictates raising only the teacup to drink, not the cup and saucer, and to return the cup to the saucer after each sip, according to Kelly. And avoid another major gaffe -- slurping.
Some advise that turning one's back on the queen is also not done. And the Obamas excelled in that department, turning their backs instead on the cameras to talk to the royal couple, and facing the media only when it came time to take pictures.
Details are scanty on what took place in the meeting behind closed doors and whether the Obamas made any gaffes. But simply put, the queen is probably used to world leaders making those by now.
"These things have been done so many times, she's a master at this point," said Charles Kidd, editor of Debritts Peerage and Baronetage, a British firm specializing in etiquette publications.
The queen has met all sitting U.S. presidents during her reign, except one.
For his part, President Obama was overtly excited about the meeting.
As he said during his meeting with Brown: "There's one last thing that I should mention that I love about Great Britain, and that is the queen. And I'm so very much looking forward to ... meeting her for first time later this evening. And as you might imagine, Michelle has been really thinking that through because I think in the imagination of people throughout America, I think what the queen stands for and her decency and her civility, what she represents, that's very important."