They went to Victoria’s Supreme Court to stop State Coroner John Cain forcing them to give evidence at the inquest into the deaths of residents during a 2020 outbreak.
They lost their case in a decision handed down by Justice Stephen O’Meara on Monday.
Their barrister Ian Hill QC had argued that WorkSafe was using the inquest as a “dress rehearsal” for criminal proceedings against the pair.
Cain had ruled that the pair must give evidence, but offered the protection that nothing they said could be used against them in a criminal case.
Hill argued Cain could be perceived to have formed an alliance with family members of residents who died, including several who were vocal about their desire for Kontis and Kos to give evidence.
But to suggest the experienced judge could be perceived as having formed an alliance with family members was “ludicrous”, according to government barrister Edwina Brown.