The bodies of two babies have been mixed-up in a Sydney hospital, which resulted in one of the children being accidentally cremated, New South Wales health authorities have said.

Chief Health Officer Dr Kerry Chant said the babies — one stillborn and one miscarried — had been mixed-up by staff at Royal North Shore Hospital last year because a blanket obscured an identification tag.

Both of the babies' bodies were then cremated, despite the family of one of the children requesting a burial.

The health department apologised to both of the families and offered grief counselling.

In a statement, the Royal North Shore Hospital said they apologised at the time.

"A full investigation was undertaken and the families were fully informed of its outcome," it said.

"A number of measures have since been put in place to avoid a similar mistake being repeated in the future."

Pressure mounting on Health Minister

It is one of three separate incidents that emerged during budget estimates on Tuesday.

Last year, at the same hospital, a woman discovered her 89-year-old mother's body had been incorrectly labelled during a final viewing, which had happened only by request.

The daughter asked hospital staff if she could take one final photo of her mother and realised that the incorrect identification tags were on the body.

Dr Chant told the committee hearing it was a "near miss of a catastrophic outcome", but it could have been worse if the body was buried.

Health Minister Jillian Skinner apologised to the family but said it rarely happens.

"I'm devastated for them and I'm really sorry that such an incident occurred," she said.

"There was another one involving the mother of a deceased infant that occurred about 15 years ago.

"So it is a very rare event. Tragic, but rare fortunately."

A third incident uncovered in estimates on Tuesday involved the exhumation of an incorrectly identified body in south western Sydney.

The details are unlikely to ease the pressure on the embattled Health Minister.

At the hearing's opening, Premier Mike Baird continued to back Ms Skinner.

"Jillian Skinner continues to do a good job," he said.

Ms Skinner is already weathering calls for her to resign after one baby died and another suffered suspected brain damage after they were given nitrous oxide instead of oxygen, in another Sydney hospital.