Federer secured his place with a win over America's John Isner Thursday.
"You just feel bad really. But relief because it's finally over... maybe I just got really lucky today," Federer said talking to media.
"I don't want to say that I feel invincible right now, but I feel good," he added. "I'm not the only guy with confidence ... It's a complete open tournament, I think. Everyone has a very good chance of going all the way," he said.
World No.1 Federer will take on Argentina’s Juan Martin Del Potro to win a place in final while Williams faces top women’s seed Victoria Azarenka in a repeat of her Wimbledon semi-final last month.
Williams, seeking the first singles medal of her career, has lost only 13 games through four rounds.
She has won 11 consecutive matches this summer at the All England Club, including her fifth Wimbledon title a month ago