Last week, the Federal Bureau of Investigation completed a report on sexual misconduct allegations against Mr Kavanaugh - but the findings have not been released to the public.
Would Senate Majority Leader Mitch McConnell (R-KY) be breaking precedent if he allowed a Supreme Court nominee a hearing and a vote in 2020? With courtroom security tight, there were no disruptions by protesters during the arguments, as there had been during Kavanaugh's confirmation hearings.
Kavanaugh, in contrast, is expected to be a more decidedly conservative vote, tilting the court right for decades and leaving Roberts as the justice closest to the ideological middle.
As the newest member of the court, Kavanaugh will take on a few special jobs.
"We wish you a long and happy career in our common calling", Roberts said.
Kavanaugh was quick to weigh in, asking his first question of a lawyer representing a defendant about 20 minutes into the first argument. "The justices do not sit on opposite sides of an aisle".
At one point, Kavanaugh could be seen having a lighthearted exchange with liberal Justice Elena Kagan, seated next to him.
The cases challenge the types of crimes that qualify as violent felonies under that law and can lead to 15-year mandatory minimum sentences for a defendant. In this case, the issue turned on whether a Florida robbery statute would call for an enhanced sentence. But for Donald Trump, the goal of occasion wasn't the formalities.
The justices themselves have expressed concern in recent years about public perception of the court.
Bulgarian Investigative Journalist murdered
Bulgarian Prime Minister Boyko Borissov: "I am convinced it is a matter of time before the murder would be revealed". Victoria Marinova , a 30-year-old Bulgarian journalist, was murdered in the town of Ruse, Buglaria on Saturday.
"Thank you Susan Collins for thoughtfully reviewing Judge Kavanaugh's judicial record and weighing the evidence, and for being a reasonable voice during this incredibly divisive time", Carrie Severino, the group's chief counsel and policy director, said in a press release accompanying the news.
The judge was confirmed by the Senate on Saturday, in a 50-48 vote that largely followed party lines.
Kimmel had some choice words about Trump's performance during Monday's televised ceremony, especially when the president proclaimed that Kavanaugh had been "proven innocent" of Dr. Ford's assault allegation.
He later wrote in a newspaper opinion piece that he regretted some of his comments. Joe Biden in 1992, where he argued that if a Supreme Court seat became vacant, then President George H.W. Bush should not nominate someone until after that year's election.
"Four of the female clerks currently serving at the Supreme Court were with him at the DC Circuit, and now he's tipped the balance at the court for the first time with an all-female clerk class", she said.
Mr Kavanaugh actually joined the Supreme Court on Saturday.
Kavanaugh described the confirmation process as "contentious and emotional", but said he has "no bitterness".
"The president really demeaned the confirmation process, insulted and attacked not only Dr. Ford but women who were speaking out", she said.
"Those who step forward to serve our country deserve a fair and dignified evaluation, not a campaign of political and personal destruction based on lies and deception", Trump said. "I think, given our divides, it will pretty much fall predictably between those who are for and those who are against", Clinton said.