US Lab Quest Diagnostics says it intends to appeal the judgement in the case of Ruth Morrissey.
Ms Morrissey was diagnosed with cervical cancer after her smear tests were misread.
She is now terminally ill.
In last week's ruling, the High Court said labs should have "absolute confidence" before declaring smear tests clear from abnormalities.
However medics say while screening saves lives, it's never going to be 100% reliable.