Second seed Federer toyed with Gilles Simon for much of Wednesday's rain-affected quarterfinal, prevailing 6-3 7-5 6-2 while Murray enjoyed a similarly comfortable afternoon in southwest London against Vasek Pospisil.
The Scot advanced 6-4 7-5 6-4 on Center Court over the Canadian, a loser to one of the Murray brothers for the second time in three days.
Having been deprived of a blockbuster Murray-Rafael Nadal quarterfinal after Spain's 14-time grand slam winner fell to Dustin Brown in the second round, tennis fans can now look forward to an intriguing clash between two of the men's game's 'Big Four.'
Another member of the 'Big Four,' defending champion Novak Djokovic, later cruised against U.S. Open champion Marin Cilic 6-4 6-4 6-4. But there was drama in one quarterfinal, with 21st seed Richard Gasquet upsetting French Open champion Stan Wawrinka of Switzerland 6-4 4-6 3-6 6-4 11-9 in a battle of one-handed backhands to ensure a pairing with Djokovic.
Federer leads Murray by the slimmest of margins in their often fascinating duels, 12-11, but the more famous Swiss has won three in a row and inflicted a devastating 6-0 6-1 defeat on the world No. 3 when they last met at 2014's season-ending championships about 15 miles northeast of Wimbledon.
'He left everything out there, making the World Tour Finals,' Federer told reporters Wednesday. 'I think when I played him, he was a bit cooked, to be honest.
'I played a great match, but it was not the Andy that usually comes up and shows up.'
Murray was indeed a different player. The World Tour Finals marked the end of a turbulent, inconsistent campaign following back surgery at the conclusion of 2013.
Having seemingly fully recovered from the injury, and now settled in his coaching setup, Murray is adamant that he's playing better than even in the summer of 2013 when he won Wimbledon to end Britain's 77-year men's singles drought. A year earlier in a turning point for Murray, he beat Federer at the 2012 Olympics to win the gold medal on Wimbledon's grass.
Murray might be the crowd favorite playing at home, but it won't be by much against the universally adored Federer.
'Roger's obviously extremely popular everywhere he goes,' Murray told reporters. 'So it might not be as partisan a crowd or atmosphere as some matches that I play here. But it will still be an excellent atmosphere, so I'll still get, you know, a boost from the crowd, I'm sure.'
Asked to pick a favorite, Djokovic said it was '50-50.'
'...Roger is maybe better ranked than (Murray),' said Djokovic. 'An incredible history of success in Wimbledon. Andy has been playing some of his best tennis this year.
'I think it's going to be a really good match.'
Federer found himself in the unfamiliar confines of Court One in a Wimbledon quarterfinal, although that didn't stop Rod Laver -- the last man to achieve the calendar-year grand slam in 1969 -- from taking a courtside seat. David Beckham and the Duke and Duchess of Cambridge, William and Kate, rooted for Murray on Center.
In Federer's box was actor and occasional Wimbledon visitor Bradley Cooper.
With his dazzling shotmaking and variety, Federer's game is all Hollywood.
Simon, whose counter-punching style mirrors Murray's, was largely defenseless in their first encounter on grass. Federer struck 11 aces and 36 winners overall as he reached a 10th semifinal at Wimbledon to move into sole possession of second among the men in the Open Era behind Jimmy Connors' 11.
'From the first point of the match he served perfect,' Simon, appearing in his first grand slam quarterfinal in six years, told reporters. 'He never gave me any occasion.
'It was hard to have a grip on him.'
Failing to serve out the second set at 5-4 wasn't an issue for Federer -- who had won 116 consecutive service games, dating back to the first round of the German grass-court tournament where he triumphed last month.
The 33-year-old broke straight back for 6-5, won the first point and closed out the set following the second of two rain delays.
Four of his five matches at Wimbledon this year have wrapped up in 95 minutes or less, so fatigue certainly won't be a problem against the younger Murray.
It was at this stage in 2014 that Murray exited Wimbledon in an uncharacteristically flat outing against Grigor Dimitrov.
He was the heavy favorite against the 56th-ranked Pospisil, who was making his debut in a grand slam quarterfinal, and put in an efficient display to avoid being upset again.
Even reading notes during changeovers couldn't revive Pospisil, who lost to Jamie Murray in doubles Monday -- when he played 10 sets of tennis in singles and doubles.
A day after completing a comeback, five-set win over Kevin Anderson, Djokovic faced no such danger against the similarly towering Cilic. He improved to 13-0 against the Croat, whose season has been blighted by a shoulder injury.
Djokovic was likely rooting for Gasquet, since he owns a 11-1 record against the Frenchman and thumped him at the French Open last month. Wawrinka, by contrast, downed Djokovic in the French Open final for a second grand slam title and their previous four grand slam matches had stretched to five sets.
Content to play more defensive than Wawrinka, Gasquet nonetheless attacked when given the opportunity. Both players ventured to the net and one backhand exchange in the first game of the fifth set -- ending with an angled Wawrinka winner -- had the fans on Court One off their feet.
It was an entertaining, epic contest.
Gasquet couldn't serve out the affair at 5-3 in the fifth yet his chance as it turned out wasn't gone. Wawrinka struggled with his backhand return throughout and he netted one when holding a break point at 9-9.
Wawrinka then trailed 0-40 in the ensuing game and after saving two match points, hit a powerful serve down the middle. Gasquet managed to keep his floated reply in play, allowing Wawrinka to send his backhand long after 3 1/2 hours.
But unsurprisingly the Swiss still have a familiar face in the semifinals.
Read: Serena battles past Azarenka
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