The court ruled the Northern Ireland Human Rights Commission (NIHRC) had no legal standing to bring a challenge to the abortion law, saying it could only have been brought by a woman impacted by the abortion ban.
Together For Yes co-founder Ailbhe Smyth said she welcomed the ruling because the majority of the judges involved in the case said Northern Ireland's laws were "incompatible" with human rights.
The Court was deciding specifically whether this should be abolished in cases of rape, incest and fatal foetal abnormality.
Unlike in other parts of the United Kingdom which are covered by the 1967 Abortion Act, a termination in Northern Ireland is only permitted if a women's life, or permanent mental or physical health is at risk.
"The commission had argued the law criminalizes vulnerable women and girls and subjects them to inhumane and degrading treatment in violation of the European Convention on Human Rights", NPR's Debbie Elliott reports.
"I am relieved to hear the highest court in the land has recognised that Northern Ireland is in breach of human rights for people who find themselves with fatal foetal abnormality and have said that the law needs to be changed, so we will keep going until we get that change", she added.
Last month, when Ireland voted in a landslide referendum to overturn its abortion ban, Prime Minister Leo Varadkar called it the "culmination of a quiet revolution".
May has insisted that abortion is a devolved issue and should be dealt with in Stormont.
"We acknowledge that this is a technical victory; however, it is important to note that the Supreme Court has dismissed the case brought by the Human Rights Commission. What now will happen is that we have issued proceedings in today in Belfast in Sarah's name to have that formal declaration made and our work will continue at Westminster to ensure that long overdue legislative change happens", she said. But Justice Brian F Kerr said that they "must be worthy of close consideration by those in whose power it lies to decide whether the law should be altered".
When Ireland replaces the constitutional ban with more liberal legislation after a debate in parliament, Northern Ireland will be the only remaining region in Britain and Ireland to outlaw the procedure. In doing so, it has made clear that there is no human right to abortion.
Caroline Simons, legal consultant to LoveBoth, said: "We do not believe however that there is any obligation on the Government to legislate for unrestricted abortion in the first 12 weeks of pregnancy. Change on this is needed and needed now", said Breedagh Hughes, Royal College of Midwives Director for Northern Ireland. "I hope this ruling means that things will change so no more women have to go through what I, and so many others, already have". Following her death, people took to streets to call for immediate reforms in the country's abortion laws.
"When examined closely, providing abortion on such grounds would fly in the face of the Taoiseach's commitment that any new law would be restrictive and that abortion would be rare".