Federer dropped a set for the first time in the championships, but victory in a second-set tie-break proved the turning point as he reached a 35th grand slam semi-final with a 3-6, 7-6, 6-4, 6-4 victory.
The 32-year-old said: “I know there’s pressure [to win Wimbledon], but the confidence is there. There is a chance now to go a step further because you trust your game, that’s where I am right now.”
Federer’s last-four opponent will be No9 seed Milos Raonic, who reached his first ever grand slam semi-final with a 6-7, 6-2, 6-4, 7-6 win over wildcard Nick Kyrgios.
Kyrgios had shot to prominence 24 hours earlier with victory over world No1 Rafael Nadal and felt those exploits contributed to his quarter-final defeat.
He said: “I was struggling about halfway through the second set. I had nothing left to give.”
No1 seed Novak Djokovic went the full distance before overcoming Marin Cilic 6-1, 3-6, 6-7, 6-2, 6-2.
World No3 Simona Halep plays 20-year-old Eugenie Bouchard in today’s semi-final following respective wins over Sabine Lisicki and Angelique Kerber.
ORDER OF PLAY
Centre Court (from 1pm)
Lucie Safarova (CZE)  v Petra Kvitova (CZE) 
Eugenie Bouchard (CAN)  v Simona Halep (ROU)