Sisters Mary Doogan and Concepta Wood maintained that being required to supervise staff involved in abortions was a violation of their human rights.
They claimed that, as conscientious objectors to the process, they should be entitled to refuse to delegate, supervise and support staff taking part in terminations or providing care to patients during the process.
The midwives took their case against NHS Greater Glasgow and Clyde to the Court of Session in Edinburgh last year but lost.
In February, a judge ruled that the mid- wifery sisters did not have direct involvement and dismissed the action.
The women said then they were "very disappointed and greatly saddened" by the decision.
Their appeal is being heard by Lord Mackay, Lady Dorrian and Lord McEwan at the Court of Session. The court heard claims it should be up to an individual's conscience to determine what amounts to "participation" in the abortion process.
Ms Doogan, 58, and Ms Wood, 52, were employed at the Southern General Hospital in Glasgow.
