A woman imprisoned for 20 years over the deaths of her four children, and pardoned in June, saw her convictions quashed by New South Wales state on Thursday, with her lawyer saying she plans to claim "substantial" compensation.

Kathleen Folbigg was convicted in 2003 of murdering three of her children, and of manslaughter in the death of her fourth. Folbigg maintained her innocence and said the children had died of natural causes over a decade, from 1989 to 1999.

In 2019, an initial inquiry into the case reaffirmed Folbigg's guilt. But in 2022, a second inquiry led by a former chief justice found new evidence suggesting two of the children had a genetic mutation that may have caused their deaths.

Folbigg was released from prison in June this year after being pardoned.

"I am grateful that updated science and genetics has given me answers as to how my children died," an emotional Folbigg told reporters outside a criminal appeals court in Sydney.

"However, even in 1999, we had legal answers to prove my innocence. They were ignored. And dismissed," she said. "The system preferred to blame me rather than accept that sometimes, children can and do die suddenly, unexpectedly, and heartbreakingly."

Folbigg's lawyer, Rhanee Rego, said her legal team was preparing a claim for "substantial" compensation for her wrongful imprisonment.

"I'm not prepared to put a figure on it, but it will be bigger than any substantial payment that has been made before," she said.

The case, which relied predominantly on circumstantial evidence, caused controversy among scientists and statisticians, some of whom were part of the campaign to secure Folbigg's release.

"Although there was new scientific evidence (in 2019) ... basic scientific principles were not adhered to from the time of trial," said Anna-Maria Arabia, chief executive of the Australian Academy of Science. "Make no mistake ... without law reform, these sorts of miscarriages of justice will continue.