Such is the anticipation that Friday's other semi-final between defending champion Novak Djokovic and Richard Gasquet is in danger of becoming a warm-up act.
Second seed Federer, the seven-time champion, boasts a narrow 12-11 lead in his decade-long rivalry with Murray.
But he is 4-1 to the good at the Grand Slams, including a four-set win in the 2012 Wimbledon final which delivered his 17th and most recent major title.
Murray, five years the Swiss star's junior, won their only other clash at the Grand Slams -- a five-set semi-final thriller in Australia in 2013.
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Federer, runner-up to Djokovic 12 months ago, will be playing in his 10th Wimbledon semi-final and 37th at all the majors.
Murray, who became Britain's first men's Grand Slam title winner since Fred Perry in 1936 when he lifted the Wimbledon title in 2013, is in his sixth All England Club semi-final and 17th at the majors.
"There was a lot on the line with Andy. I think he was going for his first Wimbledon in '12. So obviously it was always going to be tough. He had lost some majors before that (three finals in total)," said Federer.
"Then the Olympics was just a different vibe altogether. I was a bit weathered but Andy played as good a final as you can play."
Federer reached Friday's semi-final with the minimum of fuss, dropping serve just once to Gilles Simon in the quarter-finals which ended a streak of 116 service holds stretching back to the first round in Halle last month.