updated 07/24/2013 AT 7:00 AM ET
•originally published 07/24/2013 AT 8:00 AM ET
And now for great-granny!
Baby Cambridge woke up in a palace Wednesday and soon afterwards had a visit from a queen. And not just any monarch – this was proud Queen Elizabeth, meeting her great-grandson and third in line to her throne.
The visit, to Nottingham Cottage at Kensington Palace, was the latest for Prince William and Kate’s newborn son, following those of his grandparents, who saw him shortly before he left St. Mary’s Hospital in Paddington, west London, Tuesday.
The Queen visited the cottage – the couple’s temporary home while their main digs Apartment 1a are being renovated – for about half an hour.
She was seen smiling proudly as she passed reporters at the palace entrance in her distinctive green Bentley.
Many insiders believe the young parents, both 31, might discuss possible names with the 87-year-old as she cooed over the latest addition to the Royal Family, who has yet to be named.
The couple have said that they have had friends texting them names over recent months, but William hinted when they left hospital Tuesday that they were “having a proper catch-up” with him as they decide on a name.
Over at Buckingham Palace, where the Queen was told of the birth of Baby Cambridge in her private apartment Monday, she had been described as “delighted” with the news of the successful delivery. (William and Kate’s newborn is the Queen’s third great-grandchild, following the daughters of William’s cousin, Peter Phillips.)
Her mood was said to be matched throughout the grand corridors of the Palace, where the atmosphere was considered “calm” and one of “excitement” as staffers and members of the family awaited the good news.
“Thrilling,” was how one aide summed it up to PEOPLE.
Meanwhile, PEOPLE has also learned, Prince Harry has been by to meet his nephew.