PRINCETON — Hours after Supreme Court nominee Brett Kavanaugh's spot on the nation's highest court was all but solidified, two of the court's three female justices appeared on stage at Princeton University for a talk — and Kavanaugh's name wasn't uttered once.

But Justices Elena Kagan and Sonia Sotomayor decried the politicization of the court, stressed the importance of rising above partisanship in their relationships with their colleagues, and expressed concern that a true centrist won't sit on the court moving forward.

"It's an incredibly important thing for the court to guard, this reputation of being fair, of being impartial, of being neutral," Kagan said, "and of not being simply an extension of the terribly polarized political process and environment that we live in."

Sotomayor added that political polarization "has hurt the court a lot, and will continue to do so."

The justices appeared Friday evening in front of an estimated audience of 3,000 as part of Princeton's "She Roars" conference, aimed at celebrating women. It was moderated by Heather Gerken, the dean of Yale Law School, Kavanaugh's alma mater. She hasn't taken a public position on his nomination, though she previously called for additional investigation into sexual misconduct allegations against him.

The talk took place the same day Kavanaugh cleared a key procedural vote, and hours after Sens. Susan Collins (R., Maine) and Joe Manchin (D., W.Va.) committed to voting in favor of confirming the nominee, all but assuring his spot on the court. A final vote could take place as early as Saturday.

If confirmed, Kavanaugh will replace Justice Anthony M. Kennedy, who retired, and whom Kagan praised alongside former Justice Sandra Day O'Connor as centrists.

"Going forward, that sort of middle position," she said, "it's not so clear whether we'll have it."

Both justices tiptoed around making comments about their colleagues, saying a healthy working relationship with the other justices allows them to more often find common ground when deciding cases.

"We live in this world where it's just the nine of us," Kagan said, "and if you hold grudges or if you have a bad relationship with one of your colleagues, then in the next case and the next case and the next case, you have not much of a chance of persuading that colleague."

Added Sotomayor: "We have to rise above partisanship in our personal relationships. We have to treat each other with respect and dignity and with a sense of amicability that the rest of the world doesn't often share."

She went on to specifically describe Justice Clarence Thomas, a right-leaning jurist who famously faced allegations of sexual harassment while going through the confirmation process, as "exceedingly caring," saying, "He and I haven't voted together on hardly anything, but I know that inside of him there is a goodness."

Kavanaugh spent the last two weeks defending himself against allegations of sexual misconduct, including those lodged by Christine Blasey Ford, who testified publicly before the Senate Judiciary Committee that Kavanaugh sexually assaulted her when they were both in high school. The FBI reopened its background check investigation into Kavanaugh this week, and senators reviewed a confidential report detailing that investigation Thursday.

Kagan, a 1981 Princeton grad, and Sotomayor, who graduated in 1976, were both nominated by President Barack Obama and confirmed by garnering votes from Democrats and some Republicans.

The pair were mentioned last week while Kavanaugh was testifying before the Senate Judiciary Committee when Sen. Lindsey Graham (R., S.C.) told the nominee and Democratic members: "When you see Sotomayor and Kagan, tell them that Lindsey said hello, because I voted for them. I would never do to them what you've done to this guy. This is the most unethical sham since I've been in politics."