Lawyers for the trust claimed an order should be made against Norman and Mildred Wylie because their planned litigation had been “hopeless”.
But a judge in Belfast declined to take the exceptional step of awarding costs without any determination on the merits of the couple’s abandoned case.
The Wylies run two homes - Bawn Cottage in Hamiltonsbawn and Hebron House in Markethill.
They commenced legal action against a ban on new admissions imposed by the trust in 2013.
The prohibition was brought in amid allegations of the financial abuse of six vulnerable people.
Mr and Mrs Wylie deny any wrongdoing or irregularities, insisting their professional reputation is being ruined.
A police investigation resulted in a decision not to prosecute.
Proceedings were lodged by the couple in a bid to have the trust’s decision declared unlawful.
But earlier this year they dropped the planned application for leave to seek a judicial review.
Counsel for the health authority returned to the High Court this week to ask for costs of the case.
Following submissions, however, Mr Justice Colton decided against making such an order.