Murray endured an afternoon of hard labour against David Ferrer, eventually edging a step closer to becoming Britain’s first male singles finalist at the grasscourt slam since 1938 with a grinding 6-7 7-6 6-4 7-6 victory.
With the twice former champion long since departed it will be the imposing frame of Jo-Wilfried Tsonga standing in his way after the Frenchman beat German Philipp Kohlschreiber 7-6 4-6 7-6 6-2.
Before Murray’s energy-sapping win over seventh seed Ferrer, Federer treated Britain’s Prince William, his wife Kate, and a host of former greats such as Andre Agassi and Rod Laver, to a vintage display of shot-making to thrash Mikhail Youzhny.
More of a procession than a tennis match, a supreme Federer, bathed in rare shafts of sunshine, won 6-1 6-2 6-2 to record a 14th win in 14 meetings against the unfortunate Russian. Not even words of comfort from the Royal Box could save Youzhny.
“I asked Andre (Agassi) what I should do,” said the hapless Youzhny who must have been tempted to scratch the word “help” into the hallowed turf having etched “sorry” into the French Open clay during a beating by Ferrer last month.
Defending champion Djokovic had a few anxious moments against Florian Mayer, the second German in the last eight, as he reacquainted himself with outdoor tennis after playing his three previous matches under Centre Court’s roof.
Once he recovered from an early break, however, the top seed found his rhythm to claim a dominant 6-4 6-1 6-4 victory.
Federer, who will reclaim the world No. 1 ranking if he beats Djokovic and goes on to match the seven titles of Pete Sampras, has never played the Serb on the lawns.
“I’m just happy that I’m around further than I’ve been the last couple years,” the 16-times major winner, who was stopped in the quarter-finals in 2010 and 2011, told reporters.
“I’m happy I’m feeling good again. It gives me confidence going into a big match against Novak.”
Djokovic, who has conceded just one set so far, said Federer would be a daunting foe.
“Roger has been on the top of the men’s game for so long. This is where he won six titles. He definitely wants to prove himself and to everybody else that he can win it once again,” Djokovic told reporters after easing to victory on Court One.
Murray’s path to a fourth consecutive semi-final has been a treacherous one and he teetered on the brink against Ferrer before producing his best tennis of the tournament.
“I knew it was going to be tough, it was the hardest match I’ve played so far,” Murray, Britain’s equivalent of the lone ranger each year at Wimbledon, told reporters.
He had been outplayed in the first set, despite forcing it to a tiebreak, and was in deep trouble in the second as Ferrer, buzzing around the baseline like wasp at a jam jar, broke in the ninth game to serve for a two-set lead.
A rare lapse from Ferrer, who beat Murray at the same stage of the French Open last month, allowed Murray to get into another tiebreak and after trailing 5-2 he produced courageous tennis to level the match.
The third set was balanced on a knife edge until the ninth game when Murray hit a purple patch, breaking serve with staggering returns before sealing the set with a rasping ace.
Murray saved two break point at 3-4 in the second set and after a short rain delay, returned to win another tiebreak to the delight of the 15,000-capacity crowd and hundreds more watching on the screen named after Tim Henman, who also reached four semi-finals at Wimbledon.
Henman never made it to a final but Murray looks in the mood to go a step further and even become Britain’s first male champion at the tournament since Fred Perry in 1936.
“The goal now is to win the next match and get to the final for the first time. I’ve had a good run over the last few years but I’m not satisfied with that,” Murray said.
“Subconsciously I’m pretty stressed out right now, but I try not to show it.”