Lords Hamilton and Cullen told the BBC that abolishing corroboration will increase the likelihood of miscarriages of justice.
The top prosecutor, Lord Advocate Frank Mulholland, argues that the move will help remove barriers to justice for people such as rape victims.
But Lord Hamilton said: "They should retain corroboration as an essential element of our criminal jurisdiction in Scotland."
Lord Cullen said: "It's very important that (corroboration) is there and always has been for centuries as a safeguard against wrongful conviction."
The original proposal came from Lord Carloway who recommended to the Scottish Government that the provision should be scrapped.
The plan is contained in the Government's Criminal Justice Bill, currently being debated at Holyrood.
A Scottish Government spokeswoman said the removal of corroboration is supported by Victim Support Scotland and Scottish Women's Aid.
"In abolishing the requirement we are seeking to ensure police and prosecutors can focus on seeking the best quality of evidence available," the spokeswoman said.
"We consider this to be a more progressive approach than trying to meet an outdated technical requirement which is a barrier to prosecutions - particularly in sexual offence and domestic abuse cases - that would go ahead in any other jurisdiction. The Crown Office and Procurator Fiscal Service (COPFS) and Police Scotland have strongly supported this reform."
People will not be prosecuted on the evidence of one individual, she added.
"In every case investigated and prosecuted, police and prosecutors will look for evidence to support the allegation made," she said.
"Secondly, there is no evidence that any other legal system which operates without this requirement - every other jurisdiction in the western world - has a problem with this.
"Lord Carloway couldn't find any evidence of this in his wide-ranging review of law and practice and we should trust our judges, prosecutors, defence lawyers, police, independent prosecutors and juries to make right decisions based on the evidence available. And as at present, it will be necessary to prove that the accused is guilty beyond all reasonable doubt in each and every case."
Potential safeguards include changing the jury majority required for a conviction to two-thirds rather than a simple majority.