Mary Doogan and Concepta Wood, who worked as labour ward co-ordinators Glasgow's Southern General Hospital, believe their right to conscientious objection should extend to refusing to delegate, supervise or support staff looking after women having abortions.
They object on religious grounds to participating in abortion. They had set out a conscientious objection stemming from their beliefs many years ago, a measure that was recognised in the 1967 Abortion Act.
They maintained that before 2007 they were not called on to delegate, supervise or support staff dealing with patients undergoing terminations.
The women raised a judicial review at the Court of Session in Edinburgh challenging the board, which was rejected last year.
Miss Doogan, 58 of Garrowhill, and Mrs Wood, 52, of Clarkston, both Glasgow, have now appealed to three judges at the Court of Session. Their counsel Gerry Moynihan QC told the court that the case may go to the Supreme Court from either side.
He argued that "the dividing line" over what was exempt ought to be an individual's conscience.
Brian Napier QC, for the health authority, said supervisory responsibility did not trigger the right to conscientious objection. The hearing continues.