Fery also received a birthday card from the Prince and Princess of Wales.
Speaking after their interaction, he expressed appreciation for Catherine’s attendance at men’s single’s semi-finals and said it was “great to have her there” and “meet her finally”.
“She wished me good luck for the rest of the year and congratulated me for these two weeks.”
Asked whether he thinks she will take him up on the offer of playing tennis with George and Charlotte, Fery said: “Let’s see, I don’t know. Let’s see if I get the call up.”
Lord Frederick Windsor, his wife Sophie Winkleman, and Lady Gabriella Kingston were among the other members of the royal family watching the men’s single final between Jannik Sinner and Alexander Zverev on Centre Court.
They joined Australian actress Nicole Kidman, American actor Rami Malek, British singer Raye, and former world number one Stan Smith.
After Sinner won the championship for the second year in a row, Kate, who is patron of the All England Club, presented the trophy to him.
Fery, who arrived at the Championships as the world number 114 and had never advanced beyond the second round of a Grand Slam, defied all expectations to reach the semi-finals.
He will be confirmed as the new British number one and will rise to 36th in the world rankings on Monday, as well as taking home £900,000 in prize money.