On the other half of the draw, Federer will face No. 8 Milos Raonic, the first Canadian man in a Grand Slam semifinal since 1923.
Federer was broken for the first time in the tournament, and dropped a set for the first time, too, but defeated Australian Open champion Stan Wawrinka 3-6, 7-6 (5), 6-4, 6-4 in a matchup between a pair of pals from Switzerland.
In 2013, Federer lost in the second round at the All England Club.
"Last year was rough. I was very disappointed," the 32-year-old Federer said. "Went back to the practice courts. Didn't have any options left at that point."
Raonic outserved Nick Kyrgios — the 19-year-old Australian who eliminated Rafael Nadal in the fourth round — in a 6-7 (4), 6-2, 6-4, 7-6 (4) win with the help of 39 aces.
In the women's quarterfinals, No. 3 Simona Halep beat 2013 runner-up Sabine Lisicki 6-4, 6-0, and now faces No. 13 Eugenie Bouchard, who got past No. 9 Angelique Kerber 6-3, 6-4. Thursday's other semifinal is 2011 champion Petra Kvitova against No. 23 Lucie Safarova. Kvitova is the only woman left who has won a major title.
"It's a normal evolution of things," the 20-year-old Bouchard said. "As the great champions get a bit older, the new ones start coming in."
Dimitrov and Raonic, both 23, would like to see that among the men.
It's the ninth year in a row that at least two members of tennis' so-called "Big 4" — Federer, Djokovic, Nadal, Murray — made the semifinals at Wimbledon. That quartet has earned the last 11 trophies.
"The younger guys, we want to come on that stage. We strive for this. I think we're thirsty for that," Dimitrov said. "We want to prove ourselves."
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