“Thank you for cheering for my age. I really appreciate it. It’s beautiful. Makes me feel very young.
“And I guess another thing that makes me feel very young is competing with youngsters, you know, like Cobolli today - he’s who knows how many years younger than me.”
The sixth seed prepared for the contest by meeting Camilla, the wife of King Charles III, who said she was keeping her “fingers crossed” for his match.
She watched Djokovic from the Royal Box, with British actor Hugh Grant.
Cobolli showed early intent, mixing up his play with drop shots and heavy groundstrokes from his flashing orange racquet and unsettling his illustrious opponent.
Djokovic, who has reached every Wimbledon final since 2018, served for the first set at 5-3 but the Italian broke back and won the ensuing tie-break.
Cobolli, who has claimed titles in Bucharest and Hamburg this year, next had to answer the question of whether he could sustain his level against the 24-time Grand Slam champion.
But it was a different story in the second set as Djokovic broke twice to level the match in the evening sunshine.
The pair swapped service breaks early in the third set but Djokovic pounced again in the 11th game and thundered an ace as he took control of the match.
The fourth set was tight but Cobolli failed to put away a simple winner at the net in the ninth game.
Djokovic slipped and fell awkwardly when serving for the match, grimacing in pain, but got up to finish the job.
He played down the incident in his on-court interview.
“I had a nasty slip, but that’s what happens when you play on the grass,” he said.
“It did come at an awkward moment, but somehow I managed to find a good serve and close it out. Obviously, I’m going to visit this subject now with my physio and hopefully I’ll be well in two days.”
The Serb now owns the all-time record for most Wimbledon men’s singles semifinal appearances, moving one clear of eight-time champion Roger Federer, who reached the last four 13 times.
He has also reached a 52nd Grand Slam semi-final, extending his all-time record in the men’s game.
Djokovic is now within two wins of breaking his tie with Margaret Court for the most Grand Slam singles titles for any player, man or woman.
If he reaches and wins the final he will also equal Federer’s record of eight men’s titles at the All England Club.
Sinner, who beat 10th seed Ben Shelton earlier Wednesday, will offer a different level of challenge.
The top seed has won his past four matches against Djokovic, beating him in straight sets in the semi-finals of the recent French Open.
Carlos Alcaraz, who has beaten Djokovic in the past two finals at Wimbledon, takes on US fifth seed Taylor Fritz in the other semifinal.
