Queen Elizabeth II and members of the Royal Family on the balcony of Buckingham Palace (AFP)

President Donald Trump and his family got the royal treatment from Queen Elizabeth II this past week - and the American president was all in, gushing to Fox News that it was a highlight of his life, that the British monarch was "a spectacular . . . incredible woman" and that the two leaders shared an "automatic chemistry."

"There are those that say they have never seen the queen have a better time," the president said.

Well, well. The Brits may arch an eyebrow at that. Who exactly are those who say Elizabeth has never, in a 67-year reign, had a better time?

But that's what the queen does. She casts that queenly spell.

The toasts and sashes and trumpets and the men in big furry hats and scarlet tunics, which were bestowed upon Trump on his state visit on Monday, were nothing compared to the spectacle to celebrate the queen's official birthday on Saturday, when her honor guards hosted the largest military parade of the year in Britain - known as the annual Trooping of the Colour - not for a visiting dignitary, but the 93-old monarch herself.

After decades in the spotlight, the wily nonagenarian is still center stage.

The Notorious Q rules.

Her majesty, accompanied by members of the royal family, were all out in those bright dresses and uniforms for the birthday festivities on Horse Guards Parade, at which the Colour of the 1st Battalion Grenadier Guards were trooped.

Meghan, the Duchess of Sussex, who did not come out for Trump's state visit, because she is/was on maternity leave, rallied to ride a carriage with Prince Harry down the Mall, pronounced Mal in British English.

Members of The King's Troop Royal Artillery lead the parade down the Mall back to Buckingham Palace after the Queen's Birthday Parade (AFP)

As for the Queen, she rode alone in the best and brightest carriage of all, encased in glass windows, sitting on plump pillowed seats. She did the Queen wave, the upraised shake of the hand, to the thousands of her fan/subjects/tourists lining the streets.

It's a most impressive show of pageantry, and soft power, even by royal standards: 400 musicians; 1,400 soldiers dressed in their best, their helmets gleaming, their boots polished to mirror sheen; 200 horses, groomed like models walking the catwalk in Milan.

The queen carried out an inspection of her troops; there was a 41-gun salute from Green Park, another from the Tower of London; and later a gaggle of royals appears on the balcony of Buckingham Palace, cranking their necks skyward to watch a Royal Air Force fly past in jets.

Royal watchers will know that Saturday was not the queen's actual birthday. She turned 93 back in April and, presumably, celebrated privately with her family, maybe sipping a tipple of English gin and Dubonnet, insiders suggest.

But because she's the Queen, she has two birthdays, including today's public celebration aired live on the telly. For more than 250 years, the sovereign has celebrated his or her birthday alongside the military parade.

Saturday's festivities topped a busy week, which saw her majesty welcome Trump and his many family members on Monday. Then on Tuesday she welcomed the prime minister of Australia. Then she attended a massive 75th anniversary D-Day commemoration at Portsmouth on Wednesday.

Her speech there was a three-paragraph modicum of class and restraint, which ended with a single "thank you" from nations of the free world.

"When I attended the commemoration of the 60th anniversary of the D-Day Landings, some thought it might be the last such event. But the wartime generation - my generation - is resilient, and I am delighted to be with you in Portsmouth today," she said.

Next week? Visits from the kings of Spain and the Netherlands.

Elizabeth is Britain's longest reigning monarch, having taken the throne more than 67 years ago, and she is still a master at the game of this kind of diplomacy, in which there are no real "deliverables," no overt advancement of any particular policy, but instead a gloss of warm feelings, mixed with awe.

Crowds gather outside the gates of Buckingham Palace ahead of the Queen's Birthday Parade (AFP)

She clearly won over Trump during his visit. It's not an uncommon sentiment. When Barack Obama was in London three years ago, he said of the queen: "She is truly one of my favorite people."

This past week was not without its hiccups. The royal family tweeted - and then quickly deleted - a picture of Elizabeth greeting various leaders during D-Day commemorations, including the German Chancellor Angela Merkel. The tweet said that the queen was introduced to leaders "representing the allied nations." Alas, the Germans were famously on the other side during World War II.

But the queen herself seemed to hit the right notes. The events over the past week also showcased how she is increasingly yielding to the second and third generations, who have been schooled by her.

Prince Charles, who at 70 is no spring chicken, offered a glimpse of what the British monarchy would look like when he is king.

Charles hosted a tea at Clarence House, joined Trump for an inspection of the honor guard and represented the queen at a return banquet at Winfield House. Prince Andrew, Prince William, Catherine, Duchess of Cambridge, and Prince Harry were spotted at various events as well.

Charles Anson, the queen's former press secretary, said that after Elizabeth turned 90, she started to take a step back and her children began picking up some of the slack.

"It's been accepted very readily by the public," said Anson. "It's a conscious delegation - she's not cutting out of public life but she wants to undertake less engagements, which is fair enough at 93," he said.

No one expects the queen will retire from public duties like Prince Philip, the queen's gaffe-prone husband, who hung up his royal spurs two year ago. He turns 98 on Monday.

Some wondered if he should have stuck around for the recent state visit.

"You spend a lifetime cringing at Prince Philip insulting people, and the one time you want him to, he's retired," quipped Marina Hyde, a Guardian columnist.

He famously bungled his Land Rover earlier this year, suggesting that the glare from the sun stopped him from seeing oncoming traffic. Less than two days later, he was pictured driving a new Land Rover without a seat belt. Soon after the palace announced the prince had given up driving.

Asked if he thought Elizabeth would ever retire, Anson said: "No, never. . . She will delegate more and more, but she enjoys her work, she's utterly committed to it." He said that she takes very seriously the vows she made to dedicate her whole life to service, and in addition, "there's her own sense of public duty, which is particularly strong in the war and post war generations," he said.

"She's absolutely on the ball," he added. "She's still got a huge amount of energy. She's not at a reception for 30 minutes. She's there for an hour, and hour 15. But she does enjoy the support of family and spreading some of the public duties."