Whittaker edged a 3-2 split decision win against Brazil’s Keno Machado to reach the light-heavyweight last four.
McCormack, meanwhile, beat Uzbekistan’s Bobo Baturov via a 4-1 split decision to reach the welterweight semi-final, where he faces Ireland’s Aidan Walsh.
It means both Britons will leave Tokyo with at least a bronze medal.
There could be more medals in boxing for Britain, with Caroline Dubois one win away from securing one of them after a split-decision win against USA’s Rashida Ellis to reach the women’s lightweight quarter-finals.
Whittaker, from West Bromwich, will return to the ring on Sunday to fight for a place in the gold medal round.
“It was difficult, you never want to look too far ahead but I can’t help myself,” Whittaker Said.
“The people on my side of the draw are big swingers – I’m a confident, arrogant lad but I won’t lie – when I came out my belly was doing flips, my legs were gone, but as soon as the bell went it went away.
“It doesn’t matter if it was split or unanimous – a win’s a win.”
Whittaker now has his sights set on returning home with an Olympic title, adding: “I want to come back with the gold medal and become the mayor of Wolverhampton and call all the shots.”