Hillary Clinton is already well practised at royal audiences, having joined her husband - former US president Bill Clinton - and the monarch at Buckingham Palace in 1995 and 2000.
But the prospect of the Royal Household entertaining a controversial Donald Trump and his entourage could make for an interesting occasion.
Although the Queen has met every American president of her reign so far except one - Lyndon B Johnson - only two have been treated to a grand official state visit to the UK - George W Bush and Barack Obama.
It is not known at this stage whether Mrs Clinton or Mr Trump could expect a state visit invite, but a meeting with the monarch is likely to be on the cards - given the Queen’s close dealings with previous presidents. Buckingham Palace has declined to comment.
State visits are used to strengthen Britain’s relationships with countries around the world and, after the Brexit vote, could be seen as an important way of deepened ties with the US.
But they take a great deal of planning - Mr Obama’s took place more than two years after he took office - and US ones are particularly costly security-wise because of the demands of the American secret service.
• READ MORE: Insight: President Trump’s new world order
The monarch is well used to building up a rapport with American leaders, having met Harry S Truman, Dwight D Eisenhower, John F Kennedy, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Reagan, George Bush Snr, Bill Clinton, Mr Bush and Mr Obama.
She is said to have had an affectionate relationship with Mr Eisenhower who was even invited to stay at her Scottish hideaway Balmoral Castle. They met on her first state visit to America in 1957 and also later travelled on the Royal Yacht Britannia together.
The glamorous JFK and his wife Jackie dined with the Queen and the Duke of Edinburgh at Buckingham Palace in June 1961, while Mr Nixon and the Queen met at BP and Chequers.
But how will the new resident of the White House fare in their relationship with Britain’s head of state?
A hard act to follow
Whether the next American leader is Mrs Clinton or Mr Trump, they are in the unenviable position of following Barack Obama.
Mr Obama developed such a friendly relationship with the sovereign that he even dropped in to see her the day after her 90th birthday, describing her as “one of my favourite people”.
The Obamas and the Queen hit it off after a reception ahead of the G20 summit in 2009. The monarch and Michelle Obama acted like old friends when they put their arms around each other.
A successful state visit to the UK followed in 2011 and the Obamas have also forged a strong bond with Queen’s family - particularly Prince Harry and the Duke and Duchess of Cambridge.
Mrs Clinton has an advantage over Mr Trump thanks to her previous encounters.
She was pictured chatting animatedly with the sovereign at the palace in 1995, and had tea with her in 2000. They also met in the US at a return dinner hosted by the Queen when the monarch travelled to America in 2007.
Do they like horses?
The Queen loves horses - talking about them, riding them and watching them race.
When US president Ronald Reagan stayed at the Queen’s favourite home Windsor Castle in 1982, the monarch and former film star developed a bond through their passion for riding.
They rode side by side in Windsor Great Park, both looking relaxed and informal in jodhpurs and riding boots, with the Queen in her headscarf. Although the trip was an official visit, rather than a state one, Mr Reagan and wife Nancy were honoured with a banquet at Windsor.
Mr Trump likes golf - as does the Queen’s son the Duke of York - and Mrs Clinton loves to swim, but neither has a reputation as being big fans of horses.
Mrs Clinton has, however, called for an end to the slaughter of horses for human food - but the Queen’s daughter the Princess Royal has suggested that horse welfare could be improved by putting horsemeat on sale in UK supermarkets.
Don’t mess with the Queen’s home
Ahead of President George W. Bush’s state visit in 2003, the Queen put her foot down and rejected a request from his security advisers to strengthen Buckingham Palace’s walls in case of an airborne terror assault.
There was also a rather different kind of security problem associated with Mr Bush’s stay.
Daily Mirror journalist Ryan Parry sparked a major alert when he managed to become a footman at the palace using false references in the run up to the visit.
Parry claimed he was given the chance to get close enough to the Queen to have poisoned her, revealed she kept her breakfast cereal in Tupperware boxes and took pictures of the bed in which Mr Bush and his wife Laura were to sleep.
Don’t ask the Queen to intervene
The Queen apparently politely declined recently when an American citizen asked her to put Mr Trump out of the running and take back control of the US.
Surprising the letter-writer with a response, a member of the Queen’s correspondence staff wrote, on what appeared to be headed palace note paper: “Whilst your views have been noted, you will appreciate, I am sure, that there can be no question of the Queen intervening in the affairs of another Sovereign state.”
Watch out for another “Podiumgate”
When the Queen visited the US in 1991 under the presidency of George Bush Snr, the White House lawn was the scene of a gaffe.
As the monarch delivered an address, all that could be seen of her above the podium and microphones was her hat after someone forgot to put the small, raised platform in place ready for the royal VIP.