The bitter partisan fight over Mr Kavanaugh's nomination became a firestorm after sexual misconduct allegations emerged involving Mr Kavanaugh.
He tried to distinguish between President Donald Trump's nomination of Kavanaugh this year and his own decision not to have the GOP-run Senate consider President Barack Obama's high court nominee, Merrick Garland, in 2016.
Kavanaugh and his team are settling into the former chambers of Justice Samuel Alito, who moved to the offices vacated by retired Justice Anthony Kennedy. There were no disruptions by protesters during the oral arguments, with security tight in the courtroom.
Collins was a key swing vote in the battle to confirm Kavanaugh and her 45-minute speech on the Senate floor announcing her "aye" vote last week virtually ensured his ascension to the high court. Kavanaugh could serve for decades in the lifetime job.
"Brett Kavanaugh may look the part when he dons the robe, but Kavanaugh will be an illegitimate justice for as long as he sits on the Court, " said Brian Fallon, executive director of a group called Demand Justice that opposes Kavanaugh. It only takes four justices to grant cert, which means that Kavanaugh's appointment didn't force an end to the appeal. United States, a case about whether a state robbery offense should be classified as a "violent felony" under the 1984 Armed Career Criminal Act, which is a criminal sentencing law that increases prison sentences after multiple violent felonies.
Speaking before boarding the Marine One helicopter on the White House south lawn, Trump predicted the attack on Kavanaugh would cost the opposition party in next month's nationwide congressional elections. Conservative Justice Neil Gorsuch joined the court past year.
Turning to Judge Kavanaugh, he added: "You, sir, under historic scrutiny, were proven innocent" - a conclusion that will come as news to many who argued that the investigation was not thorough enough to know either way. And Saturday's vote was also a victory for the Senate, and for the integrity of our institution.
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Boarding the Marine One helicopter at the White House ahead of a trip to Florida, he branded the sexual assault allegations that threatened to derail Kavanaugh's path to the top court "a hoax" and "all made up, fabricated".
During the confirmation process, Judge Kavanaugh had appeared annoyed as he defended himself against Dr Ford's accusation, which he denies.
He later wrote in a newspaper opinion piece that he regretted some of his comments.
Kavanaugh is describing the confirmation process as "contentious and emotional" but says he has "no bitterness".
Kavanaugh hears his first arguments from the bench today, having salted away the traditional duties of cafeteria supervision befitting the tradition for SCOTUS newbies.
"You share a name with a great man who's now one of only 9 Supreme Court justices".
The appeals were brought by an environmental group and companies that supported the rule, which had limited hydrofluorocarbons used in a variety of products including spray cans and air conditioners.