The group seeks a declaration of inconsistency that the government has failed to justify the discrimination they claim they face.
The declaration would not change the voting age but instead serve as a message to Parliament that it is time for change, according to the group.
At today's appeal hearing, lawyer Jason McHerron read out an affidavit from Isobelle Smith, who said she was invested in her community, but because of her age was unable to vote.
"My voice can get lost in local issues of importance," she said.
She was able to participate in political conversations, but when it came to decisions through voting, her future was taken out of her hands, she said.
"It is young people who will live with the consequences of these actions."
McHerron said the group acknowledged the ultimate issue of whether to change the voting age was up to Parliament.
Since 2020 the group has sought a declaration from the courts, but at each hurdle has been denied.
When they took their case to the Court of Appeal in 2021, it was found the voting age provisions were inconsistent with section 19 of the Bill of Rights Act, freedom from discrimination.
However, despite a partial win, the court declined to make a declaration. Today's appeal is to seek the declaration once again.
McHerron said there was no compelling reason for the court not to make the declaration.
The group's written submissions said it was essential the court declared "the correct legal position", especially where age discrimination affects electoral rights.
Crown lawyer Austin Powell, representing the Attorney-General, said the Court of Appeal was correct to recognise it was a time for restraint in declining the group's request.
It was an issue for Parliament, and the "winds of change must blow through the electorate" before a declaration of such significance can be made, he said.
"The courts had been invited to engage in a policy-heavy, constitutionally significant question before Parliament has done so," he said in his written submissions.
Powell said this was not a suitable occasion for the court to give such a declaration.
"This is one of the rare situations where it is a question for Parliament and not the courts," he said.
However, McHerron disagreed and said it was more important than ever. He said it was a principle of comity, with the courts and legislature acting mutually.
"This is not the court straying into politics, it is just the court applying the law."
Lily Lewis, a member of Make it 16 who has been with the organisation since its inception, said it had been a long journey for the group, who had been through multiple hurdles together.
The growth of the organisation, that originally began as an idea out of youth Parliament, had reached national levels and attracted thousands of supporters.
This growth and resilience through the legal process was uplifting, Lewis said.
"I have so much pride and aroha."
Make it 16 co-director Cate Tipler said it was a significant day for rangitahi.
She emphasised that they believed it was the Government's job to justify why, in its opinion, it would breach such fundamental rights.
A formal declaration from the highest court in New Zealand would be a powerful message to Parliament, she said.
"It would force Parliament and the Government to see this as a priority and boost the movement for change."
The group, formed in July 2019 by youth activists both above and below voting age, is advocating for "more people's voices to count in our democracy", according to its website.
Local government elections will be held on October 8.