The UK's highest court will hear legal arguments on whether midwives have a right to refuse to take any part in abortion procedures on moral grounds.
NHS Greater Glasgow and Clyde appealed to the Supreme Court after judges in Scotland said Roman Catholic midwives had a right to conscientious objection.
This was despite Mary Doogan and Concepta Wood not being actively involved in terminations.
Five judges in London will hear the case. A ruling is expected next year.
Ms Doogan, from Garrowhill in Glasgow, and Mrs Wood, from Clarkston in East Renfrewshire, were employed as labour ward co-ordinators at the Southern General Hospital in Glasgow.
Caroline Wyatt, BBC Religious Affairs Correspondent
Almost 50 years after abortion became legal in England, Scotland and Wales, it remains a deeply emotive issue, both for its supporters and for those who object to abortion on conscientious grounds.
Under Roman Catholic doctrine, life begins at conception, and no human being has the right to take the life of an unborn child.
Although many Catholic women do seek abortions in the UK, the stance taken by the Roman Catholic Church has underpinned many of the pro-life groups which have challenged the legalisation of abortion and the interpretation of the 1967 Abortion Act.
This landmark case tests the balance between those whose religious beliefs do not allow them to play any part whatsoever in abortion, and the health authorities' duty under the law to enable women to have an abortion. Many Christian groups back the midwives' position.
Both are practising Roman Catholics and argued that they "hold a religious belief that all human life is sacred from the moment of conception and that termination of pregnancy is a grave offence against human life."
The midwives' counsel, Gerry Moynihan QC, told the court in the women's earlier successful appeal that the law was clear that the right to conscientious objection contained in the Abortion Act was intended to apply to the whole team whose involvement was necessary to achieve the procedure.
If the Supreme Court upholds the midwives' earlier successful appeal, it could set a legal precedent, allowing other midwives who object to abortion to take the same stance.
The Royal College of Midwives and the women's charity British Pregnancy Advisory Service have both warned that any such ruling could have severe implications for the care of women choosing to terminate their pregnancy.
They challenged whether NHS Greater Glasgow and Clyde (GGC) could require them to delegate, supervise and support staff who were involved in carrying out abortions.
The Court of Session in Edinburgh initially ruled in 2012 that their human rights had not been violated as they were not directly involved in terminations.
At the time, judge Lady Smith said: "Nothing they have to do as part of their duties terminates a woman's pregnancy.
"They are sufficiently removed from direct involvement as, it seems to me, to afford appropriate respect for and accommodation of their beliefs."
But last year, appeal court judges overturned Lady Smith's judgement, ruling the "right of conscientious objection extends not only to the actual medical or surgical termination but to the whole process of treatment given for that purpose."
NHS GGC later asked the Supreme Court to examine whether section 4(1) of the Abortion Act 1967, which provides that "no person shall be under any duty... to participate in any treatment authorised by this Act to which he has a conscientious objection", extends to labour ward co-ordinators.
The health board's appeal has been backed by both the Royal College of Midwives (RCM) and the British Pregnancy Advisory Service (BPAS), which said they were "deeply concerned" at the right to conscientious objection being extended.
In a joint statement, they said: "If this decision is upheld it will require all professional guidance to be rewritten and will enable a tiny number of staff opposed to abortion to make women's care undeliverable in some NHS settings in the UK."
Ann Furedi, the chief executive of BPAS, said the body "supports the right of healthcare professionals to conscientious objection, not least because women deserve better than being treated with contempt by those who think they are sinners."
"But ultimately a balance needs to be struck between that exercise of conscience and women's access to legal services," she said.
"There may be a small number of healthcare workers who have a conscientious objection to providing abortion care. There are far more who have a conscientious commitment to helping women who need to end a pregnancy.
"It would be grossly unjust if an interpretation of conscientious objection was allowed to stand which would disrupt services to the point that those committed to helping women were unable to do so."