Lords Hamilton and Cullen said 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 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.
"We consider this to be a more progressive approach than trying to meet an outdated technical requirement which is a barrier to prosecutions - particularly in sexual offence and domestic abuse cases - that would go ahead in any other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."
"In every case investigated and prosecuted, police and prosecutors will look for evidence to support the allegation made," she said.
Potential safeguards include changing the jury majority required to two-thirds from a simple majority.