And detectives have pledged to not give up while there is hope of knowing where they are.
William MacDowell was found guilty of murdering Renee MacRae, 36, and her three-year-old son Andrew, at the High Court at Inverness.
He was also found guilty of covering up his crimes by disposing of their bodies and destroying evidence.
The bodies of the mother and son, who went missing in the Scottish highlands in November 1976, have never been found.
Detective Chief Inspector Brian Geddes, of Police Scotland, said: “Although justice has now been done, Renee and Andrew’s bodies have not been found.
“I would urge anyone, who may have information about where they are, to come forward so they can be provided with the dignity they deserve.
“In particular, I would appeal directly to William MacDowell, to speak to us and allow us to bring closure to the family.”
The now 80-year-old killed Mrs MacRae, whom he admitted repeatedly lying to during their four-year affair, and their child Andrew at a layby near Dalmagarry on the A9, about 12 miles south of Inverness.
A huge police investigation was launched after their disappearance, with road blocks set up on the busy road in an attempt to find as many witnesses as possible.
But despite this, and investigations in 1986, 2004 and 2018, the remains of Renee and Andrew have never been found.
Operation Abermule, the latest investigation, was set up to find the murderer and to discover the resting place of the pair’s bodies almost 46 years after the crime.
So far, it has only achieved one of its aims – with MacDowell convicted of the two murders.
But Mr Geddes said he would “remain optimistic” that the bodies could still be found.
He said: “We set out with that as our objective and we, the organisation, whoever comes after me, will not give up on that until there is no longer any hope.
“And there is hope at the moment, so we’ll remain optimistic.”
The next step will be to “attempt some re-engagement” with MacDowell and “see if he’s willing to speak”, the officer added.
MacDowell, who was married while having a relationship with Mrs MacRae, who was separated from her husband, had been trying to keep their affair secret.
Mr Geddes said: “The motive we have was because the pressure was increasing on his lifestyle, or at least the circumstances that might affect his lifestyle as it was at the time, and that he had to take action to maintain that lifestyle and maintain that standard of living he had which was clearly a good standard of living at the time.”
He added: “We’d love to know more answers for the sake of the family, whether they want to know the details of what happened down there.
“But, as an investigator, we’d love to know every fact and every part of the circumstances that happened.”
The latest investigation, and subsequent court case, has involved more than 1,500 witnesses, many of them either deceased or no longer able to give evidence in court.
“There is no doubt that the team that we had from 2018 onwards uncovered evidence that hadn’t been focused on before,” Mr Geddes said.
“We have certainly improved the known circumstances around Friday November 12 and beyond.
The police officer said he could “sympathise with lots of frustrations why it’s taken so long” for a conviction.
But he stressed: “We have now achieved what we set out to achieve in 2018.
“And that’s in no small measure to what was carried out in 1976, 1987, 2004 onwards. That all helped us get to this point.”