The amendment would effectively bring Northern Ireland's abortion laws into line with the rest of the UK.
The PSNI seized a remote controlled robot that was created to distribute abortion pills with the support of two providers, Women on Web and Women on Waves.
The police seized the pills and attempted to arrest one woman who openly took the tablet.
Eleanor Crossey Malone, one of those who swallowed a pill, said she acted "in defiance of the extremely outdated, medieval, anti-choice laws that exist in Northern Ireland".
In a press release, Women on Waves claimed "the abortion pills can be supplied to women in Northern Ireland without breaking the law because the robot is operated from the Netherlands".
"We are not willing to accept it anymore".
After a tense hour-long encounter staged in an open area between the court buildings, the pro-choice activists boarded a bus.
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May has a convincing political reason, above and beyond any broad theories she may hold on proper governance, to leave the matter entirely with regional lawmakers: It was only with the support of Northern Ireland's Democratic Unionist Party that May was able to form a governing coalition after her Conservative Party suffered painful losses in last year's parliamentary elections - and the DUP is one of the region's staunchest abortion opponents.
Three women gathered in a circle and others dressed as handmaidens, in reference to the Margaret Atwood novel The Handmaid's Tale about women's rights being stripped away, stood behind them.
She said the PSNI was under enormous pressure and was aware of the worldwide pressure inspired by the repeal movement. Once legislation is passed in the Republic of Ireland, Northern Ireland will be the only part of the United Kingdom or Ireland where prohibition is maintained.
The group are also planning to take the abortion pills on a tour around Northern Ireland.
She said the Police Service of Northern Ireland (PSNI) was under enormous pressure and was aware of the worldwide pressure inspired by the pro-choice movement south of the border.
"But it's important to recognise that the people of Northern Ireland are entitled to their own process, which is run by locally elected politicians".
"The DUP is a pro-life party and we will continue to articulate our position", she added in her statement.