Power, 63, and his son Nicholas Power, 36, admitted failing to self-quarantine upon returning from Queensland on a private helicopter in October last year, an offence that carries a maximum penalty of 12 months' imprisonment.
It came just 18 months after Neville Power was appointed to head up Prime Minister Scott Morrison's since-disbanded National COVID-19 Coordination Commission.
The Powers had been due to be sentenced on Thursday in Perth Magistrates Court.
But the court was told Nicholas Power was unable to attend, prompting magistrate Elizabeth Woods to adjourn the sentencing for both men.
Their lawyer Sam Vandongen SC did not provide a reason for Nicholas Power's absence.
Neville Power, who attended Thursday's hearing, declined to comment outside court.
A police prosecutor this month said the pair's actions had put West Australians at "unacceptable risk" and a term of imprisonment was appropriate.
But Mr Vandongen urged the magistrate to instead impose substantial fines on the pair.
He also flagged they would apply for spent convictions which would allow Neville Power, the former chief executive of Fortescue Metals Group, to continue in his board roles.
Power this week stepped down from his role as Perth Airport chairman and has been granted a leave of absence from board roles with Strike Energy and disability services provider APM.
He also recently resigned as chair of the Royal Flying Doctor Service Federation.
Mr Vandongen cited a psychological report which said Power had suffered stress-induced "cognitive distortions" which had clouded his judgment.
More than a dozen personal references were submitted to the court including one from billionaire FMG chairman Andrew Forrest.
The court heard Power and his son had flown separately to Queensland in September last year, spending a week mustering cattle at the family's Bushy Park station near Mt Isa.
They flew back to WA together on a private helicopter, staying overnight in Exmouth in WA's north - where they were captured on CCTV footage moving freely around a resort while not wearing face masks - before arriving at Jandakot Airport on October 9.
Travellers from Queensland were required at the time to isolate for 14 days upon arrival in WA under the state's controlled border regime. They also had to complete G2G pass declarations advising of their recent movements.
But the pair did not make G2G applications and failed to isolate, with Neville Power joining other business elites and politicians at the Telethon Ball on October 16.
The pair each pleaded guilty to two charges of failing to comply with a direction under WA's Emergency Management Act.
Ms Woods adjourned the sentencing to March 23.
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