On Monday evening, he was the guest of honor at a ceremonial swearing-in at the White House, where Trump apologized on behalf of the nation for "the awful pain and suffering" Kavanaugh and his family had suffered.
The entirely ceremonial swearing-in, two days after he officially became a member of the high court, is unusual for new justices.
Justice Kavanaugh, 53, brought the nine-member court back to full strength after the retirement of long-serving Justice Anthony Kennedy in July.
He went on to thank President Trump for his unwavering support and cited Kennedy, for whom Kavanaugh clerked, as a role model and mentor.
Kavanaugh met with all four of them on Sunday in his new chambers, which formerly belonged to fellow Justice Alito.
The misconduct complaints concern Kavanaugh's answers about his work in the George W. Bush administration and his comments about Democrats using allegations of sexual assault against him, according to the Post. Ford told lawmakers she was "100 percent" certain Kavanaugh attacked her, but Kavanaugh forcefully denied he had assaulted her or any other woman.
In his speech at the ceremony, Kavanaugh said the emotional Senate confirmation process "tested" him, "but it did not change me". Kavanaugh had said during his confirmation hearing in September that he would hire an all female clerk if confirmed.
Melania Trump in Egypt: the pyramids in the program
US First Lady Melania Trump walks with her Egyptian counterpart Intissar Amer al-Sisi after arriving at Cairo International Airport.
During the swearing-in ceremony at the White House on October 8, Trump apologized to Kavanaugh and his family "for the awful pain and suffering you have been forced to endure".
Mr Kavanaugh said he was not bitter despite the "contentious" confirmation.
"You share a name with a great man who's now one of only 9 Supreme Court justices".
Wednesday - The court will also hear a case that asks what can be used to detain undocumented immigrants during deportation. Soon, Justice Kennedy will administer the Judicial Oath to Brett Kavanaugh, just as he did previous year for Justice Gorsuch, Trump said.
The climactic 50-48 roll call vote Saturday on Kavanaugh was the closest vote to confirm a justice since 1881. "And he's continued to do that inside the White House". But critics said Kavanaugh's demeanor raised questions about his temperament and potential political bias in deciding cases.
Kavanaugh was sworn in on Saturday evening in a private ceremony as protesters chanted outside the court building.
"America's Constitution and laws protect every person of every belief and every background", he said.
Kavanaugh posed questions to lawyers in both cases before the court, his first one coming about 20 minutes into the arguments. "This will be the first time a Supreme Court Justice has ever sworn in a former clerk to take his seat - a lovely moment which reminds us that freedom is a tradition passed down from generation to generation", Trump said.