While third seed Federer pummelled Russian 26th seed Mikhail Youzhny into submission in a 90-minute 6-1, 6-2, 6-2 masterclass on Centre Court, Djokovic also took the express route against German 31st seed Florian Mayer, recording an emphatic 6-4, 6-1, 6-4 victory on Court One.
Now Djokovic will attempt to reach his second successive Wimbledon final by extending his current winning streak against Federer to four matches in their first ever encounter at the All England Club.
The world number one has proved a thorn in Federer's side of late, beating him in the semi-finals of the US and French Opens, although the Swiss great holds 14-12 edge over their 26 career meetings.
"It's always a pleasure playing against Roger. I'm looking forward to it," Djokovic said.
"He is a great champion and has been so dominant and consistent at the Grand Slams. He is the ultimate challenge on grass courts."
While Djokovic has every reason to feel confident, Federer, who has now reached a record 32 Grand Slam semi-finals, looked in peak form as he delivered a royal command performance in front of Prince William and wife Catherine.
"I played great. Maybe my game matches up well against Mikhail," said Federer, who last won Wimbledon in 2009.
"It helps when royalty and other stars come to watch, it's inspiring and a thrill and helps tennis."
Federer, who is without a Grand Slam title since the 2010 Australian Open, cruised to a 14th win in 14 meetings against Youzhny and, just as importantly for the 30-year-old, there were no signs of the back pain which had dogged him in the fourth round against Xavier Malisse.
Federer, chasing Pete Sampras's record of seven Wimbledon titles, also put an end to a worrying sequence at the All England Club where he had been knocked out in the quarter-finals in the last two years.
Later on Wednesday, home favourite Andy Murray will attempt to reach his fourth successive Wimbledon semi-final when the world number four faces Spain's David Ferrer on Centre Court.
Murray, hoping to end Britain's 76-year wait for a male singles champion at Wimbledon, will have to improve on his last meeting with seventh seed Ferrer, which ended in defeat in the French Open quarter-finals last month.
The other remaining quarter-final on Court One pits French fifth seed Jo-Wilfried Tsonga against Germany's Philipp Kohlschreiber.
Tsonga, who beat Federer at this stage last year, is aiming for his second Wimbledon semi-final, while 27th seed Kohlschreiber will be playing in the last eight of a Grand Slam for the first time.
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