Federer beat Marin Cilic of Croatia 6-3, 6-4 Friday and will next play Murray, the two-time defending champion. Murray improved his Shanghai record to 11-0 by defeating a tenacious Radek Stepanek 4-6, 6-2, 6-3.
Djokovic easily won his quarterfinal, downing Tommy Haas of Germany 6-3, 6-3. He'll face Berdych, who outlasted Jo-Wilfried Tsonga 6-3, 7-6 (4) in the day's first match. Berdych has beaten Djokovic only once in 10 matches.
This is the first time in the four years of the Shanghai Masters the top four seeded players made it to the semifinals. That has happened in four other tournaments this year: Australian Open; Doha, Qatar; Estoril, Portugal; and Umag, Croatia.
Murray defeated Federer in their last match - the London Olympics final - and has a 9-8 record against the top-ranked Swiss. Murray also took Federer in the 2010 Shanghai final.
"I assume he's very confident right now and probably playing with a little bit less pressure," Federer said. "Then again, that can go either way. It's been a long year for all of us."
Federer played solidly, saving five of seven break-point opportunities he handed Cilic. He was broken in the fourth game of the first set and when serving for the match at 5-3 in the second.
Haas was the first player this week to break Djokovic's serve, with both breaks coming in the second set. The first break was in the second game and the other when Djokovic was serving for the match at 5-2.
"(I was) a little bit more up and down with the service games," said Djokovic, who won the China Open last week. "But generally when I needed to, I played well. Played very solid from the baseline."
Stepanek dominated the first set and never gave Murray an opportunity to break serve. Murray rebounded in the second set, breaking serve to go ahead 4-2. Stepanek had two opportunities to retrieve the service break on Murray's serve in the seventh game, but Murray kept his lead.
In the third set, the 41st-ranked Stepanek had a point on serve for a 3-1 lead, but Murray broke back. He won 20 of the last 25 points.
"I just managed to turn it around in time," Murray said. "I played actually very well I thought the last 10, 15 minutes of the match."
Tsonga was undone by two mistakes - a shaky service game that he lost at love in the eighth game of the first set and a double-fault at 4-4 in the second-set tiebreaker.
"I was feeling quite well on the court," Berdych said. "I think the biggest difference between me and Jo was I was able to take the small chances during the first and especially the second set."