Her Majesty looked very elegant and regal,its a pity that royals no longer wear tiaras when visiting the Pope!
They do, when it is a
State Visit. Note that the Pope himself also did not wear a choir dress and a mozetta. He was in his plain old daily white cassock.
When the Prince of Orange, the Prince of Asturias, Princess Máxima and Princess Letizia were at the Investiture of the Pope (
see picture, click on the picture to blow up to XXL), they were a step higher in protocol, the ladies in long and the gentlemen in white tie or ceremonial uniform, but still no diadems as this was not a State Visit, which is one step higher again.
Often a State Visit to the Holy See is a spin-off from a State Visit to Rome. Even then it depends on the willingness of the visitors to wear diadems or not. Queen Beatrix (a Protestant Queen) did not. Queen Elizabeth II (a Protestant Queen) did. Queen Sonja (a Protestant Queen) did not. Queen Silvia (a Protestant Queen) did.
I hope to see Queen Letizia, Queen Mathilde and Queen Máxima (all catholic Queens) to wear it to the utmost formality but... it also depends on the Pope. It is known that Pope Benedictus XVI wanted a smooth execution of papal protocol. The same under Pope Johannes Paulus II. The current Pope seems not to be interested at all and most likely does not care at all what his visitors wear and what Vatican protocol means. He has a lot of similarities with Pope Johannes XXIII, who was a simple man too, but the last one remained attached to the centuries old papal protocol. As long as the Pope does not make that "step up" (wearing a choir dress, a mozetta, a papal stole), the royals will also not do.