Following the ceremony she told presenter Gary Lineker backstage she was "very well" when he asked about her condition, after she was recently forced to miss two royal engagements while she recovered.
She later admitted to Paralympic athlete Martine Wright, who picked up the Helen Rollason accolade, that her time on stage had been scary.
Kate, who is an official ambassador of Britain's Olympic and Paralympic teams, stayed to meet some of this year's sporting heroes, including Sports Personality runners-up Jessica Ennis and Andy Murray, as well as unsung hero award winners Sue and Jim Houghton.
Wiggins, who this year became the first Briton to win the Tour de France, followed days later by a gold medal in the Olympic Time Trial, received 492,064 (30pc) phone votes for the main award last night.
Heptathlon gold medal winner Jessica Ennis came second with 372,765 (22pc), and US Open winner and Olympic gold medallist Andy Murray was third with 230,444 (14pc).
Double Olympic gold medallist Mo Farah missed out on an award, coming fourth with 8pc of the votes.
Accepting the award Wiggins thanked the voters, including his grandmother for pressing redial "God knows how many times".
He later told the BBC that he couldn't believe Farah had not won.
Sebastian Coe was awarded the lifetime achievement honour for his athletics career and in recognition of his role in bringing the Olympics and Paralympics to London.