Police were doing everything possible to recover the bodies, but the depth of the wreckage 60 metres below the surface made it a "very complex situation", said Waikato police Inspector Marcus Lynam.
Experts' opinions and sonar work had led them to believe the couple's bodies were with the aircraft, he said.
The couple were flying to Timaru to visit their daughter Ari in Christchurch, but never arrived. During the flight the aircraft reported engine trouble and ditched into the sea off Gannet Island.
Today shocked colleagues were coming to terms with the loss of Mr Hertz, a man described as an inspirational leader and an "honorary Kiwi".
"I think it's fair to say that the people at 2degrees are in shock. The fact that we won't see him back, or Kathy, is quite stunning, said 2degrees' director of corporate affairs Mat Bolland.
"We're going to miss Eric's leadership, friendship and dry sense of humour. He was our 'honorary Kiwi' and greatly respected by our 760 staff."
Mr Bolland talked about his plans for the long weekend during a management meeting on Thursday "and yet again Eric probably had a more exciting weekend planned than many of us.
"We know that there's been a terrible accident, and we don't know the cause."
The board and a management team are working on a plan to ensure the company continues.
However, the company's focus was on providing support to the couple's daughter, keeping their family in the US informed of the progress of recovery, and assisting police, Mr Bolland said.
Mr Hertz was an "avid" aviator with 10 years' experience, who was qualified to fly on instruments alone, and owned two planes.
"Not a beginner, and very meticulous about his flying."
The couple called New Zealand home, said Mr Bollard.
The rescue operation has now switched to one of recovery, and has been handed to police to coordinate.
"RCCNZ [Rescue Coordination Centre] have stated that the area around where debris and oil was found was extensively searched, and that had the two occupants of the twin engined Beechcraft Baron been on the surface, they would have been found," said head of the recovery operation, Sergeant Warren Shaw, of Waikato Search and Rescue.
When the Westpac Rescue Helicopter in Auckland investigated, its crew found an oil slick and wreckage about 20km northwest of the entrance to Kawhia Harbour, near Gannet Island.
The aircraft is understood to have hit the water at high speed.
