Andy Caddick was bowling the first over with the second new ball and the 82nd over of the first day of the fourth Ashes Test on Thursday when Waugh edged to Butcher who appeared to catch the ball just before it hit the ground.
Waugh, on 56, stood his ground as England appealed for the catch. The decision was referred to third umpire Darrell Hair who gave it not out after watching video replays.
The Australia captain, who finished unbeaten on 62, shook hands with Butcher during the incident.
Justin Langer (146 not out) and Matthew Hayden (102), who shared an opening stand of 195 in Australia's 356 for three on the first day's play at Melbourne Cricket Ground, said Butcher was sending the right message to cricketers worldwide.
Butcher said: "Steve asked me if I had caught it and I said I wasn't sure."
Langer said the decision had been referred to the third umpire because Caddick had appealed.
"Mark Butcher straight away said he didn't catch it so I think that showed good sportsmanship. He told Stephen he didn't catch it so to me it probably didn't need to go to the third umpire," Langer said.
"Andy Caddick might have thought it did carry. At that point the umpire said 'are you appealing?' and he said 'yes I am appealing'."
Hayden said: "It's terrific to see that in sport. I think the handshake was very reflective of the way everyone feels about the way the game should go."
Langer, 32, who reached his 13th Test century with a six off spinner Richard Dawson, said it was the most satisfying innings he could have played.
"That nice feeling...for about one or two seconds in your life you feel absolutely untouchable. It was like standing in a vacuum," Langer told a news conference.
"You know it's going for six and you know you've just got a hundred. It makes all the bad days worthwhile."
Hayden, meanwhile, said he was excited to see Waugh, 37, make a half-century when his future as a Test player was under scrutiny.
"He's a true iceman under pressure and he just came out all class today I thought. He's in good touch."
England assistant coach Graham Dilley said the tourists had generally performed well under difficult circumstances.
"They (Australia) are great players, aren't they? They have spells where they take the game away from you," Dilley told a news conference.
"I think there were actually some good things for us to take out of it."