18 November 2016 06:42 pm
The girl, who was terminally ill with a rare cancer, was supported by her mother in her wish to be cryogenically preserved - but not by her father.
She wrote to the judge explaining that she wanted "to live longer" and did not want "to be buried underground".
The girl, who died in October, has been taken to the US and preserved there.
A High Court judge ruled that the girl's mother should be allowed to decide what happened to the body.
The details of her case have just been released.
The teenager, who lived in the London area and cannot be named, used the internet to investigate cryonics during the last months of her life.
The judge, Mr. Justice Peter Jackson, visited the girl in hospital and said he was moved by "the valiant way in which she was facing her predicament".
His ruling, he said, was not about the rights or wrongs of cryonics but about a dispute between parents over the disposal of their daughter's body.
It was brought to court for the first time on 26 September and the judge made his decision on 6 October.
Mr. Justice Jackson said the case was an example of science posing new questions to lawyers.
The girl died peacefully in October knowing that her remains would be preserved, but the judge said there had been problems on the day she died.
He said hospital staff and bosses had expressed concerns about the way the process of preparing her body for cryogenic preservation had been handled.
This was carried out by a voluntary group in the UK before her body was flown to the US for storage.
He suggested that ministers should consider "proper regulation" of cryonic preservation for the future.
What is Cryonics?
Cryonics is the process of preserving a whole body in the hope that resuscitation and a cure are possible in the distant future.
It is a controversial procedure and no-one yet knows if it is possible to bring people back to life.
There are facilities in the US and Russia where bodies can be preserved in liquid nitrogen at very low temperatures (less than -130C) - but not in the UK.
The cost of preserving the body for an infinite amount of time in this case was £37,000.
The teenager's letter to the judge
"I have been asked to explain why I want this unusual thing done.
"I am only 14 years old and I don't want to die but I know I am going to die.
"I think being cryopreserved gives me a chance to be cured and woken up - even in hundreds of years' time.
"I don't want to be buried underground.
"I want to live and live longer and I think that in the future they may find a cure for my cancer and wake me up.
"I want to have this chance.
"This is my wish."
An artist's impression of how cryogenically preserved bodies might be stored in the future.