Midwifery sisters Mary Doogan, 57, and Concepta Wood, 51, said being forced to supervise staff taking part in abortions violated their human rights.
But a judge at the Court of Session ruled the midwives did not have direct involvement in terminating pregnancies.
A preliminary hearing in the appeal will be held in July.
A further hearing is then expected to take place early next year.
The women had sought to challenge NHS Greater Glasgow and Clyde on the issue because of their "conscientious objections".
At the Court of Session in Edinburgh in February, Lady Smith ruled Ms Doogan, from Garrowhill in Glasgow, and Mrs Wood, from Clarkston in East Renfrewshire, were removed from direct involvement in procedures and as such were afforded appropriate respect for and accommodation of their beliefs.
The health board maintained that the Abortion Act did not confer on the midwives any right to refuse to delegate, support or supervise staff providing nursing care for women going through abortions.
Two Roman Catholic midwives who lost a legal battle to avoid taking part in abortion procedures have appealed against the decision.