"I could ask anyone where - would you rather have law enforcement rummaging through your desk drawer at home or rummaging through your iPhone.
"I mean there's much more private information on the iPhone than in most desk drawers, so yes, the fourth Amendment should apply there."
He talked about electronic devices in which there could be up to 200,000 patents applying and the need for lawyers to be able to clearly present cases to the courts.
And he also referenced new types of search equipment.
"There are devices now that can allow law enforcement to see through walls, heat imaging and all this kind of thing.
There's much more private information on the iPhone than in most desk drawers, so yes, the fourth Amendment should apply there.
"What does that do to a body of law that has developed from common law days in England about when you can search a house?" he asked.
"If you're standing on a street and you're applying [the method] is that the same thing as kicking down the door and seeing it?"
None of the nine judges on the Supreme Court claimed to be an expert in the area.
"That is going to be a particular challenge for us to make sure we understand the technology...and a challenge for the lawyers to make sure they do a good job of presenting it to us."
Justice Roberts was being questioned before an invited audience in a university lecture theatre by the Dean of Law and Pro Vice-Chancellor Professor Mark Hickford.
Many members of the New Zealand judiciary were present as were lawyers, law students, and senior members of the public service.
Roberts conducted the oath of office for President Donald Trump when he was sworn in on January 20. He was not asked any questions about Trump.
But Roberts did volunteer some criticism about the how confirmation of judicial nominations had become political.
I think we are experiencing a bit of a rocky road because the judicial process has become overly politicised
"I think the system that the founding fathers of my country established is a good one - that the President, the chief executive officer of the Government answerable to all the people is the one that makes the nomination, but that a separate body, the legislative body, the senior legislative body has to give its assent. I think that is a wonderful and important check and a balance approach - each of the two political branches coming together in selecting the membership of the third branch.
"That's the theory. In practice, I think we are experiencing a bit of a rocky road because the judicial process has become overly politicised," he said.
"It didn't used to be that way as a general rule. I think there is a lack of understanding about what sort of things people should be looking at when they are deciding who should be a judge particularly in the confirmation process.
"Judges are not politicians and so they shouldn't be scrutinised as if they were. You are not electing a representative so you're not entitled to know what their views on political issues are.
"You are selecting someone who is going to objectively and fairly apply the law that binds the other political branches.
"Yes, of course the judges have a significant impact on political life but they are supposed to do that only as judges, only as necessary to decide a particular case and according to the law, not according to personal policy preferences."
He went through some of issues that should be canvassed during confirmation.
"Do you think they have a fair understanding of how the constitution works? It is not simply a question of saying 'well here are the words and this is how it applies.'
"Do you understand what it means to have separated authority which we have in the United States and is certainly not as strict and formal in New Zealand?
"What do you look at when you have a question about whether Congress has exceeded its power under the Congress clause?
"What sort of things do you consider when the issue is that the President doesn't have particular authority, not 'what is your view on this - whatever is the sensitive political... issue of the day."
"I think if the process were more focused on those other things, it would be more useful - closer to what the founding fathers had in mind."
Roberts did not talk specifically about his Supreme Court colleague Ruth Bader Ginsberg who last year talked with concern about the possible election of Trump as President. But as part of her escape plan she joked "Now it's time for us to move to New Zealand."
Republicans are demanding she recuse herself from any upcoming cases on Trump's travel ban.
But when asked to reflect on the relative roles of the political branch and the judicial branch, Roberts said: "I think it is very important for the judiciary to appreciate they are not part of the political process and it is very important for the public to understand that.
"Your authority to affect the political branches of government is limited by the necessity to decide a particular case.
"It is that responsibility that carries with it the authority to interpret the constitution. You don't have a free-ranging licence to opine on what you think the constitution means."
Roberts graduated from Harvard Law School in 1979 and in 1982 he was a law clerk for Associate Justice William Rehnquist on the Supreme Court, who went to become Chief Justice.
He said that Rehnquist would like to consider cases by walking around the grounds of the Supreme Court and talk about them and test ideas which had been "extremely exhilarating for a young student."
They would often be stopped by visitors to Washington who would want their photo taken in front of the court.
"So dozens and dozens of people have pictures of themselves in front of the Supreme Court around the country and have no idea it was taken by the Chief Justice of the United States."
Justice Roberts was nominated as Chief Justice in 2005 by President George W Bush.
It was a controversial appointment at the time because he was so young, only aged 50 and he had been a judge for only two years.
He had originally been nominated to replace one of the Supreme Court Associate judges who was retiring. But Rehnquist died before his nomination was confirmed and Bush then nominated him as Chief Justice.
Trump's nominee for the Supreme Court, Neil Gorsuch, was confirmed several months ago meaning there is now a five-four balance between those perceived as conservatives, including Roberts, and liberals.
