No births had been registered, and there was no supporting evidence in medical records.
But the court heard and saw other evidence that a child or children do exist.
Lady Emma Arbuthnot described it as a “perplexing” case and acknowledged the family court lacked the tools to investigate thoroughly.
The judgement was published, external on Wednesday after a hearing that took place in May.
The ex-husband is applying for contact with the child. The judge said there will be another hearing “in due course” to determine what happens next.
On a video link in May, I watched the last hearing in this long dispute, which began more than three years ago.
The couple had married in 2019, but separated in 2020. The ex-husband said the twins were born the following February.
On opposite sides of the grand courtroom, in the Royal Courts of Justice, the smartly-dressed couple sat as far apart as they could.
Neither had lawyers, which meant they had to argue their own case, and question witnesses themselves.
At times, the ex-wife looked anxious and upset, especially when a psychotherapist gave evidence under oath.
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