Madelaine Cave and Donald Holm, former US Consul General in Scotland, were in Amsterdam when their baby Meghan died at 15 days old because of an undiagnosed heart condition.
The couple decided to have her cremated in Edinburgh and planned to scatter her ashes on the Lammermuir Hills, where Mr Holm had proposed.
Meghan was cremated at Mortonhall on June 8, 1994. But her parents, now divorced, were told the installation of new burners meant the baby girl would just "vaporise" because of the temperature, so there would be no ashes.
They have written separately to both the US Consulate in Edinburgh and the US Embassy in London, demanding pressure on the Scottish Government to discover what happened to their daughter's remains.
Mrs Cave, who lives in North Berwick, East Lothian, with her second husband and two daughters, said : "Both of us were really upset but we ultimately reconciled ourselves to the idea that she was in the ether. We were pleased she was not in the soil and mixed with dirt. Yet now we discover that is exactly what is likely to have happened to her."
The city council would only confirm that new burners were installed in Mortonhall in 1994 and that an audit of records should establish what happened to Meghan's ashes.
Eight separate families have alleged breaches to the 1935 Cremation Act at Mortonhall after failing to receive their babies' ashes.