Ledger has won a Critics Choice Award and a Screen Actors Guild nomination
Heath Ledger's parents say his posthumous Golden Globe for The Dark Knight should go to his 3-year-old daughter Matilda.
Speaking from the late actor's family home in Perth, Australia, Ledger's father Kim said he watched the awards ceremony with "bittersweet pride".
The actor died of an accidental drug overdose prior to the film's release.
His role as the Joker has also won a Critics Choice award and is expected to get an Academy Award nomination.
Ledger received a standing ovation from the audience when he was named best supporting actor. The award was accepted on his behalf by director Christopher Nolan.
Kim Ledger was moved by the standing ovation which greeted his son's award
"A standing ovation breaks you up," said Kim Ledger.
He added: "That really goes to the heart, you know."
In an interview with People magazine, Ledger's mother, Sally Bell, said: "I should imagine that eventually it will be going to Matilda.
"It will belong to her because she is part of him."
She has described the recognition the 29-year-old actor had been getting for his work as an "emotional rollercoaster".
"There is a lot of emotion tied up in this and we have to deal with that emotion first before we can relax and enjoy the moment," she said.
Matilda is the daughter of Ledger and actress Michelle Williams.
Nolan said Ledger would "be eternally missed but never forgotten"
The couple separated a few months before his death and the child is being raised by Williams.
Meanwhile, the 2009 Golden Globes saw a 27% slump in viewers since the last ceremony in 2007.
It averaged 14.6 million viewers, down from 20 million two years ago and the lowest since 1996.
Last year's ceremony was cancelled due to the Hollywood screenwriters strike.