Coventry City Council has been ordered to pay £100,000 towards parents' court costs after it tried to put three of their children into care.
Judge Clifford Bellamy said the council had "fallen below accepted standards" in its decision making process.
The council had accused the parents of pretending their children were ill, saying they had been subjected to unnecessary medical tests.
It later withdrew its care applications and said it regretted its mistakes.
The judgement was made in February, but the judge has just allowed the council to be named after an application by was made by the BBC.
The children's parents also told the judge they wanted the council to be named.
Colin Green, director of children, learning and young people at Coventry City Council, said it had been a complex and difficult case but the children's welfare had always been at the heart of it.
He said he accepted that mistakes were made which the council regretted and that it would not be appealing against the order to pay the contribution towards legal costs.
The court heard that in June 2008 the council applied for care orders for three children, known as X, Y and Z.
In June 2009, in a final threshold document, the council said the parents had subjected all three to unnecessary hospital admissions, medical examinations and tests and that they had lied about or exaggerated the children's symptoms.
In January 2010, the authority gave notice it intended to withdraw proceedings for X and Y, but would continue with Z.
In February, it gave notice it wished to withdraw the proceedings relating to Z.
Judge Bellamy said the council had abandoned all of the matters it relied upon in its original documents by belatedly acknowledging it had little or no material in which to satisfy the criteria set out in its threshold document.
He also said the council had not taken steps to evaluate information in relation to the children's involvement with health services and that it had relied completely on a medical report, when it should have raised shortcomings in the report with its author.
"In my judgement, the local authority's conduct of this case falls outside the band of what is reasonable," he said.
The council must pay £100,000 towards the family's estimated costs of almost £400,000, paid for with taxpayers' money through the Legal Services Commission.
The figure was a "matter of concern" in a case where "at the 11th hour" the authority sought leave to withdraw its application for care orders for the three children, now aged now aged 12, nine and eight.
In response, the council said it particularly regretted its analysis of the medical report.
"This assessment, the judge concluded, did not include sufficient evidence of fabricated or induced illness as had been concluded by the medical expert," Mr Green said.
He also said the case was not reviewed effectively at key points and that the council had not "stepped back" to see the whole picture.