He will play No. 7 seed Marin Cilic, who outslugged No. 24 Sam Querrey, 6-7 (6), 6-4, 7-6 (3), 7-5. If Federer wins, he will become the only man to win eight Wimbledon singles titles, and he will add one more to his record of 18 major championships.
He came into the tournament among a group of four men considered the favorites, including No. 1 Andy Murray, No. 2 Novak Djokovic and No. 4 Rafael Nadal, the so-called Big Four. But only Federer, who skipped the clay-court season, made it to the semifinals, and he did so looking as sharp and fluid as he did in the last decade when he vacuumed up the bulk of his trophies.
He has not lost a set in his first six matches at the All England Club, and he has lost only two matches all year.
Most times when Federer takes the court, fans will witness an array of some of the most graceful and even stupefying shots, especially on grass, where he has excelled more than any other surface.
All of those were on display against Berdych, from Federer’s balletic backhand to some spirit-crushing, acutely angled forehands. During the second set, Federer stretched to reach a deep ball on his backhand that seemed destined to become a Berdych point.
But using only his wrist, Federer slapped at the ball on a short hop and did not just put it back in play — he hit a winner past a stunned Berdych at net.
Federer also dazzled with some running forehands, twice deflating Berdych by reaching a ball that stretched out wide in the alley and firing back a piercing forehand down the line for a winner.
Berdych played well, forcing Federer to engage in two tiebreakers, and he even provoked some Federer frustration. Federer had a break point at 2-2 in the third set, able to sniff a decisive moment that he could ride to victory.
But he hit a running forehand into the net and yelled out an invective in Swiss German. It was the only brief moment of frustration for Federer, who found a way to win the most important points.
After winning the final point, Federer raised both hands and smiled as the fans saluted another win.
In the other half of the draw, many observers were intrigued before the tournament by the prospect of a potential semifinal between Murray and Nadal.
But that matchup never happened because of their early departures. But Cilic and Querrey gave the fans a compelling performance, anyway, pounding serves, driving ground strokes with authority and, when necessary, demonstrating a feathery touch at net.
Neither had ever made a Wimbledon final, and Querrey, the 29-year-old from California, was in dogged pursuit of his first final at any Grand Slam event after entering 42 of them. But he will have to wait some more.
He made his first quarterfinal here a year ago and his first semifinal this year, so the arrow could be pointing up.
“Pencil me in for the final,” he said with a big smile, “and hopefully that will happen.”
Cilic, in his 11th try, set a men’s record for most Wimbledon appearances before reaching the final. That bested Pat Rafter, who reached the final in his eighth Wimbledon.
Cilic, a 28-year-old Croatian, is 1-6 against Federer, but the one win was significant. Cilic overwhelmed Federer in the semifinals of the 2014 United States Open, which Cilic went on to win for his only Grand Slam title.
Before the tournament began, Federer said he thought Cilic had a chance to go deep into the tournament. Cilic was pleased to hear such praise, long before he knew that he would oppose Federer in the final.
“That gave me a little bit more belief, a little bit more confidence, that, you know, players and people around are also seeing that I’m in a great form, that I’m able to do great things,” Cilic said after his quarterfinal win.
Cilic had a favorable draw. The highest seed he had to play was No. 16 Gilles Müller, who upset Nadal.
Querrey, the first American man to reach a Grand Slam singles semifinal since Andy Roddick at Wimbledon in 2009, had played three five-setters in a row entering this match. The last ousted the top-seeded Murray in the quarterfinals.
Cilic and Querrey had met four times before Friday, and Cilic had won them all. One of those matches, a third-round encounter at the All England Club in 2012, went 17-15 in the fifth set and is the second-longest Wimbledon match at 5 hours 31 minutes.
This one went only 2:56, but Querrey was up a break in the fourth set and the match had the feel of a five-setter. But Cilic broke back and then broke Querrey again, at 6-5, to win.
The final shot was another mighty forehand down the line, followed by a loud scream for everyone on the grounds to hear, perhaps even by Federer, waiting in the wings for No. 19.
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