The pope presented the British monarch with the blue sphere for Prince William and his wife Catherine's 8-month old baby during an unusual exchange of gifts between the Anglican and Catholic leaders.
"It's for the little boy," Francis said, to which the queen replied: "That's very nice, he will be thrilled by that when he's a little older."
The orb is an emblem of royal power which the ancient Romans used to represent the universe, before it was adapted by Christians who added a cross on top to represent the world under Christianity.
There was a bit of confusion over protocol, before the queen's husband Prince Philip told the pope: "You go first, you need to show us where to go."
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The atmosphere was relatively informal, with a smiling queen dressed in a summery lilac with white gloves rather than the traditional black outfit or veil required of women meeting the pontiff on more formal occasions.
"I've brought something from all our estates for you personally," the queen said, while the 77-year-old pope looked rather taken aback by the whiskey handed to him by Prince Philip.
He looked better pleased with the honey, which the queen said came "from my own garden."
The queen also presented the Argentine pontiff with photographs of herself and Philip in silver frames -- a traditional gift she herself apologised for, saying: "l am afraid we have to give photographs."