Wearing an emerald green floor-length dress, Kate presented cyclist Bradley Wiggins with the top award and Lord Sebastian Coe with the lifetime achievement honour at London's ExCeL Centre.
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.
The Duchess, 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 (30%) phone votes for the main award last night.
It was more than 7% more than heptathlon gold medal winner Jessica Ennis, who came second with 372,765 (22%), and 15% more than US Open winner and Olympic gold medallist Andy Murray, who was third with 230,444 (14%).
Double Olympic gold medallist Mo Farah missed out on an award, coming fourth with 8% of the votes, a total of 131,327.
Accepting the award from the Duchess, who did not speak, Wiggins thanked the voters, including his grandmother for pressing redial "God knows how many times".
He also praised his supporters and Team Sky colleagues who helped him win the Tour de France before saluting the other Olympians.
He later told the BBC that he couldn't believe Farah had not won.
The 32-year-old said: "It has been incredible. To do this and be part of this after what everyone achieved tonight makes it more special.
"To sit in the crowd and listen to Andy then Jess be announced, well my thoughts were Mo Farah had won it. For him to not get a look-in is incredible.
"It is something to tell my kids because I think Mo will go down in history like Lord Coe."
Lord 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 and their success.
Fighting back tears he said he was flattered and honoured to win the award.
"I'm also incredibly lucky because, for the larger part of my life, I have woken up each day knowing that sport was going to shape that day.
"I have been incredibly lucky, as someone who has competed, trained, supported and, in the last few years, delivered."
He added that he shared the trophy with the millions of supporters, spectators, volunteers and athletes that were involved with the Games.
Kate had not been seen in public before last night since leaving the King Edward VII's Hospital in London on December 6, where she received three days of treatment for a condition known as hyperemesis gravidarum, which leaves expectant mothers so ill they cannot keep food or liquids down.
Kate was ordered by doctors to have a period of rest at her home at Kensington Palace after her recent spell in hospital and was unable to attend a Centrepoint Royal Albert Hall fundraiser and the British Military Tournament in the last few weeks.
The Duke of Cambridge missed the event as he remains in Anglesey in his role as an RAF search and rescue helicopter pilot, a spokesman added.