Murray was bidding this fortnight to win his second title at the All England Club and looked in excellent form heading into the semi-finals.
However Federer outclassed the Scot to win 7-5 7-5 6-4 and book a Sunday showdown with Novak Djokovic.
Federer was aggressive from the outset and served brilliantly on Centre Court, offering Murray only one break point in the opening game, before breaking his opponent at the end of each set.
“I definitely don’t feel like I played a bad match,” Murray said. “He served fantastic, apart from the first game where I had the chance there.
“I didn’t really have any opportunities. That puts pressure on you. The pressure builds throughout the set that way.
“Obviously I got broken right at the end all of the sets but I didn’t actually play a bad match. I played pretty well.”
Federer set a new record by reaching 116 consecutive service holds in the previous round, before being broken for the first time in the tournament but to no avail by Gilles Simon. And the number two seed was dominant again, producing 20 aces against Murray, who is considered one of the best returners in the sport.
“That’s definitely the best he’s served against me,” Murray said.
“Sometimes the stats come up on the court. He was serving like 80 per cent in the first set, then he was in the high seventies for most of the match.
“When he was missing the first serves, I was winning over half of the points.
“But I don’t know how many times in the match he missed two first serves in a row, it wasn’t very often.
“It’s tough to gain much momentum that way.
“I’ll have to have a think about it, because maybe I could have returned better, but it did feel like he served extremely close to the lines today.”
Federer also felt his serve was key to the outcome.
“Andy’s been playing very well for the season and there’s so much expectation riding on the match that you try to focus and keep it up,” Federer said.
“It got really tough. I’m unbelievably happy. I maybe didn’t show it as much because the crowd went silent a little bit. People may have expected it to go to four or five sets, me as well.
“I played so well on the biggest occasion today and that’s why I got it.” Discussing where he won it, Federer said: “I think on my serve again. I’ve been serving very well for the entire tournament.
“I kept the pressure up, I went for my shots. I kept pushing forwards, stayed focused and it all worked out very well.”
A thrilling 10th game in the second set eventually went Murray’s way, as he faced up to a host of set points and defended each one, before dropping serve in the 12th game.
“I was screaming inside of myself,” said Federer. “Those were set points as well – 5-4, love-40. I thought I didn’t play badly under those circumstances. Andy was able to elevate his game because I was playing at my very best.
“That was huge for him but still I was able to make the difference right after.
“I kept the pressure up and then pounced when the chance was there.”
Federer now meets Novak Djokovic, who dismissed Richard Gasquet to set up the chance to match Boris Becker’s three Wimbledon titles 30 years on from his German coach’s breakthrough triumph.
Top seed Djokovic stormed past Frenchman Gasquet 7-6 (7/2) 6-4 6-4 to book his 17th grand slam final appearance, and the opportunity to defend his 2014 title.
The Serbian admitted he was “living the dream” in victory. If you look at the names of the legends and elite group of players who are playing the finals of this great event, it’s a great honour and privilege to be out there, but I need to keep on going,” said Djokovic.
Djokovic can also mirror another of Becker’s Wimbledon exploits by retaining his title
“I’m definitely living the dream, here at Wimbledon on the most renowned tennis court in the world.
“I try to take the best of myself and I have a responsibility to play well - and I’m just glad to reach another final.”
Looking ahead to the final, Federer said: “Novak’s been the best player for a few years now and has made it difficult for players to win big tournaments.