Federer, the silky, stylish Swiss, is the favourite to prevail but Australia's Lleyton Hewitt loves nothing more than spoiling the party -- and he has won eight of the pair's 12 previous meetings.
Certainly Federer knows he is in for a battle.
"Yeah, well, for sure a very tough match," he said. "I'm going to play a player who's got a lot of experience.
"Lleyton will be extremely tough because he won here in the past. Everybody knows what great matches we had."
Although Hewitt has won two-thirds of their matches so far, Federer has won the two most recent -- at the Australian Open en route to the title and on Hamburg clay last month.
He is in spectacular form and has not had his serve broken all tournament.
"I have to say every match so far on grass has been, you know, quite unbelievable," he said.
"I've always played great tennis. There's not a match where I remember I've played bad tennis and came through. I always played very good.
"I think this is good looking ahead to the tournament because from here on only tough opponents will come my way."
They do not come any tougher than Hewitt who imposed on Federer a heartbreaking five-set defeat from two sets down in the Davis Cup semi-finals last year.
PRETTY CONVINCINGLY
He knows he can beat Federer and is determined to do so.
"Yeah, I believe I can beat him," the seventh seed said. "You know, it's going to be an extremely tough match. He's the best player
"Yeah, he's number one in the world for a reason. And, you know, he's going through the draw pretty convincingly at the moment.
"So I'm the underdog for sure. But I believe in my ability, and I've played well enough against him in the past.
"At the Australian Open, I felt like I had a lot of chances. I felt like really the first set and a half, I was a better player.
"But he's an extremely good player. When he gets on that run, he's very hard to stop. You know, I'll try and hang in there anyway."
Tim Henman will act as Federer and Hewitt's warm-up act on Centre Court.
The Briton, hoping to become the first home-grown man in 68 years to win the singles, takes on Croatian Mario Ancic. Victory will see Henman into his fifth Wimbledon semi-final -- he has never reached the final.
In other men's matches Andy Roddick and Sjeng Schalken clash while Sebastien Grosjean meets Florian Mayer.
Two women's quarter-finals are also scheduled at the All England Club.
Amelie Mauresmo and Paulo Suarez meet while Serena Williams and Jennifer Capriati clash in a repeat of their French Open quarter-final last month.
On that occasion Capriati won.
Serena has won nine of their 15 meetings, but Capriati has won the last two.
"It's good," Serena said. "I think we definitely have a nice rivalry going on... solid, you know?
"So it's definitely good... I like it."
Capriati said: "We have been really close every time, you know? And I guess just the last couple times I took advantage of her not playing that much tennis.
"It's just about me... playing the ball out there. It's never really been about the person. It's just my tennis against the other person's tennis."
