A woman who wants to use her dead daughter's frozen eggs to give birth to her own grandchild is to find out if she has persuaded leading judges to allow her to continue her legal battle.
The 60-year-old, whose daughter died of cancer, lost an action at the High Court last year.
Two Court of Appeal judges were asked at a recent hearing in London to grant permission to the woman and her 59-year-old husband to challenge the June decision of Mr Justice Ouseley to dismiss the case.
Lord Justice Treacy and Lord Justice Floyd are to give their decision on Wednesday.
During the High Court proceedings, Mr Justice Ouseley was told that the daughter, who can only be referred to as ''A'' for legal reasons, was desperate to have children and asked her mother to ''carry my babies''.
Her parents, who are referred to as "Mr and Mrs M", challenged an independent regulator's refusal to allow them to take the eggs of their ''much-loved and only child'' to a US fertility treatment clinic to be used with donor sperm.
The Human Fertilisation and Embryology Authority (HFEA) said the eggs could not be released from storage in London because A did not give her full written consent before she died at the age of 28 in June 2011.
Mr Justice Ouseley heard that A would have been ''devastated'' if she had known her eggs could not be used.
But the judge ruled that the HFEA had been entitled to find the daughter had not given ''the required consent''. He declared there had been no breach of the family's human rights.
He said: ''I must dismiss this claim, though I do so conscious of the additional distress which this will bring to the claimants, whose aim has been to honour their daughter's dying wish for something of her to live on after her untimely death.''
It was thought that if the case had been won, Mrs M could have become the first woman in the world to become pregnant using a dead daughter's eggs.
Jenni Richards QC, for the parents, told the appeal judges there was "clear evidence" of what A wanted to happen to her eggs after she died.
She submitted that "all available evidence" showed A wanted her mother "to have her child after death".
She argued: "We say an appeal would have a realistic prospect of success."
The mother, who attended the brief proceedings at the Court of Appeal, said afterwards that she was "hopeful" the court would give permission to appeal. She pointed out that she was aged 55 when the legal process began.