The Hollywood stars faced Dawnette Knight, the woman accused of making the threats as they gave evidence in a Los Angeles court.
Knight, 32, is charged with 25 counts of stalking and threatening Zeta-Jones between January 2003 and May 2004.
Recounting his wife's terror after she received three death threats in one night made in calls to a hotel in Amsterdam in May, Douglas said: 'She called me on her way to the airport. She was hysterical and concerned that she had to keep putting her head between her legs. She was fainting and could not get any air. She showed all the signs of having a nervous breakdown.'
He said he first became aware of the threats after the receptionist of a hotel he owned in Bermuda took a call in which a death threat was made against his wife. Though 'shocked, scared and stunned' to keep the threat to himself to avoid upsetting his wife and creating 'a furore or gossip,' Douglas said.
But he then found that 14 'disgusting and extremely violent letters' had been received by his father, Kirk Douglas. 'I was deeply concerned for him,' Douglas said. 'He is 87
'The bitch will be shredded to pieces like Sharon Tate was. This is going to be entertainment history,' said one letter, referring to the actress -- Roman Polanski's wife -- murdered by the Charles Manson gang.
'See ya at the funeral,' said another, which referred to a funeral for Zeta-Jones.
In her testimony, the Oscar-winning actress recalled how at one point she feared having a heart attack or a stroke because of the death threats contained in the letters and telephone calls, said CNN.
She was 'shocked at the violent, horrific, satanic desire that someone would want to do that to me. A total stranger,' Zeta-Jones said. 'I have never had a death threat in my life and this will affect me for the rest of my life,' she said.
Knight was arrested last month at her Beverly Hills home. If convicted, she faces a maximum jail sentence of 19 years. Her lawyer Richard Herman said outside the court that he had attempted to resolve the issue with the Douglases by apologising and promising that Knight would cease all contact, but their response had been 'inappropriate.'
Denying that Knight had been stalking Douglas, he said: 'There were never any threats, only friendly overtures.'