Murray lost 7-5 7-5 6-4 to the former world No 1, who will tackle top seed and defending champion Novak Djokovic in Sunday's final.
The 17-time Grand Slam champion rolled back the years with a sublime display to reach his 10th final and on this evidence he will take some stopping as he outclassed his opponent on Centre Court.
Federer fired 11 aces in the first set and 20 over the full course of the match, winning a remarkable 84 per cent of his first serve points.
"I played pretty well but he served really well," Murray said in his press conference. "I could have done more returning-wise a few times.
"I don't know if it was close to his peak, you'd have to ask him, but that was definitely the best he's served against me. He clearly deserved to win the match.
