Anderson's serve is highly respected at this level, but he managed to meet the mark with an average of only 56 per cent of his first serves over the first two sets.
By the end of this quarterfinal, a stiff drink seemed more appropriate than a serving of strawberries and cream. Djokovic broke Nishikori's serve seven times, and finished with six aces.
The 20-times grand slam champion blew a third-set match point before succumbing 2-6 6-7 (5-7) 7-5 6-4 13-11 to big-serving South African Kevin Anderson in a four-hour, 14-minute quarter-final thriller on Tuesday.
"I think it was great quality tennis and in the final set there were some incredible points", said 2008 and 2010 champion Nadal. Djokovic last appeared in the semifinals at Wimbledon in 2015, when he won.
It was the second time Federer dropped a two-set lead at Wimbledon - after a reverse to Jo-Wilfried Tsonga in 2011 - and the fifth time he lost at a major when holding a match point.
The 36-year-old Swiss ace came into Wimbledon as the favourite to win a ninth title and retain his crown from last year.
He came into the match having won 32 consecutive sets at Wimbledon, a run he stretched to 34 before faltering. A double fault was then compounded by another exhausted forehand into the net by Federer.
Raonic has the fastest serve of this year's Wimbledon at 147 miles (236.5 kilometres) per hour, while Isner is just behind on 144mph (231.7kph).
Anderson had failed to take a single set off Federer in their previous 4 meetings.
Meanwhile, after dropping the second set to Nishikori, Djokovic wrested back the momentum for good in the third, coming from 0-40 down at 2-2 to hold serve.
Roger Federer revealed he was disappointed and rued missed chances following his five-set shock defeat to South Africa's Kevin Anderson in Wednesday's Wimbledon quarter-final in London. In tough times you can sort of rely on "hey, I feel like I'm a better tennis player, I'm going to get through". For me, this is very hard to understand.
The Centre Court spectators, who included the Duchess of Cornwall, Rory McIlroy and Sir Richard Branson watching on from the Royal Box, were wowed by two highlight-reel rallies in the first five games. I felt like I did some good business here in the past already So I'm all right.
Federer, Wimbledon's greatest male champion, was greeted warmly Wednesday by Court One ticket holders who never imagined they'd have a chance to see him in person.
He enjoyed a 6-3, 3-6, 6-2, 6-2 victory over Japan's Kei Nishikori. Djokovic, a 12-time major champion, had not reached the final four of a Grand Slam event since the 2016 US Open.
Perhaps a one-on-one lesson could be in the offing at the All England Club next year, though, given how Federer keeps racking up major titles, don't expect him to explore a late-career change in sport! Honestly, I think I love being around here. Not just an experience, but a challenge that I've set for myself.
"Anything could have happened, so this is a big achievement for me to get to the semi-finals at Wimbledon".