One of the babies was wrapped in a newspaper published in 1945. The other was encased in towelling in a suitcase.
It is understood the pensioner, from Hoo, near Rochester, Kent, was receiving treatment in hospital when her son went to the house to tidy up on Monday. He discovered one of the bodies in a bedroom wardrobe.
Police were called and the other body was found.
A post-mortem examination has failed to discover how the babies died and further tests are now being carried out.
Detective Inspector Andrew Dolden, of Kent Police, said: 'This is a sad case, and I will be speaking to the lady who lives at the house.'
He said both children were thought to have been under a year old when they died. A neighbour of the woman said the son who found the bodies was 'very upset'.
She said the woman, who was her best friend, had worked as a home help and had travelled the world with her husband, who was in the Royal Navy, before his death 10 years ago. They had lived in Hoo for about 15 years.
''She told me everything, but never said anything about the babies in her bedroom,' the neighbour added.
She said that the woman was taken to hospital with broken limbs after a recent fall.
The woman had spoken of wanting other children, but said after giving birth to her son - now a father of three - she was not able to have any more.
A report was being prepared last night for the Crown Prosecution Service, which would decide whether charges would follow.
Both babies came from separate pregnancies.Reuse content