Williams, whose sister Venus is in the other semi-final against Elena Dementieva, must overcome the world 133 to reach her first final here since 2004.
On that occasion she lost to Maria Sharapova but this year she looks in good shape to add to her previous titles in 2002 and 2003.
"I would never sit here and say Venus is the favourite for a tournament when I am still in the draw," Williams said. "That's not me. I always believe that I am the favourite.
"Will it be an all-Williams final? I surely hope so and I have got to say I believe so. But now I am just fighting to win my next match."
Radwanska, who beat fourth seed Svetlana Kuznetsova in the fourth round, made a determined start to their quarter-final on Centre Court.
Even when the Pole was broken at 1-1, she continued to match Williams shot for shot and they shared some thrilling rallies as she immediately pulled level.
Williams is chasing her third Wimbledon title and first since 2003
The sheer power of Williams' groundstrokes began to tell as the set progressed and she took control of the match when she broke again to take a 4-3 lead.
Radwanska battled on, however, and stubbornly forced the American to serve out for the set.
But that resistance was nowhere to be seen in the second set and Williams was soon two breaks up at 3-0.
She produced her best tennis of the tournament as she racked up the three games she needed for victory in double-quick time and will be in confident mood ahead of her semi-final.
"I feel like I stepped up a notch today, especially with my serve," Williams added.
"That was the turning point of the whole match. I placed them well and that is how I am used to serving so I need to keep that going.
"I expected her to hit some good shots, which she did, but I played the extra shot when I had to."
Radwanska admitted she was outclassed, saying: "Serena was serving unbelievably today, especially in the second set when she could hit four aces in a game. She didn't give me a chance.
"When she is playing like that it is very tough to play against her and she was too good for me."
But Zheng will also have reason to be optimistic after another impressive display helped her get past Vaidisova.
It is uncharted territory for the 24-year-old from Chengdu, who had never previously been past the third round at a Grand Slam and who missed the whole of 2007 with an ankle injury.
I have not thought any of my matches have been easy but I have just tried my best and I have just kept going. I cannot believe I have got this far
That absence saw the doubles specialist's singles ranking slip from 27 to outside the top 100, but this success is still unprecedented and completely unexpected.
Her attacking and tenacious style was again effective against Vaidisova but her resilience was just as important in a tight first set.
Vaidisova's only double-faults of the set both resulted in her service being broken but she had four break points of her own that Zheng defended each time.
The second set was just as close with both players making mistakes and exchanging early breaks before Vaidisova moved 6-5 up and eventually served out to level despite the best efforts of Zheng.
There was little to separate the players at the start of the decider either but, once Zheng broke to go 3-1 up, she did not look back.
More errors crept into Vaidisova's game and she could not stop Zheng from closing out victory in one hour and 53 minutes.
"Did I think I could reach the semi-finals when I was given a wildcard? No," Zheng said.
"I have not thought any of my matches have been easy but I have just tried my best and I have just kept going. I cannot believe I have got this far.
"Serena is a two-times winner and a very prominent player on grass - I am in the semi-finals for the first time.
"In 2004, I lost to her in the first round when she was the defending champion. I hope I do better this time."
Zheng, who was born in Sichuan, the province where around 70,000 people died as a result of May's earthquake, has decided to donate some of her prize money to victims in China.
"I would like to give the all prize money but cannot," she said.
"I need to give back to something like the tennis association. Of course I will donate all my portion. Apart from that, I will do as much as I can to help the Sichuan region people because I'm from Sichuan province, as well.
"After going back after Wimbledon, I will do more charity work and encourage more people to come to support the stricken region and hope people from Sichuan will have their new homes as soon as possible."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.