Lord Neuberger said the case focused on "the process by which that result can lawfully be brought into effect".
The Supreme Court president promised a decision "as soon as possible".
The hearing ended with the government's lawyer arguing ministers have the authority to trigger Brexit.
The case centres on whether the UK government has the power to serve notice of its intention to quit the EU under Article 50 of the Lisbon Treaty or whether, as various campaigners have claimed, it must seek Parliament's authorisation.
The first case to be heard before all Supreme Court 11 justices, it has pitted some of the leading figures in the legal world against each other and included arguments from Scotland, Wales and Northern Ireland.