Milwaukee, Wisconsin (CNN) Supreme Court Justice Brett Kavanaugh stressed judicial independence and "allegiance to the Constitution" in his first major appearance outside of Washington since his contentious confirmation last October.

Speaking at a conference of judges and lawyers in Milwaukee on Monday night, Kavanaugh also declared, "It's important for judges not be in a bubble."

Kavanaugh appeared on stage in a hotel ballroom with his predecessor, retired Justice Anthony Kennedy, a centrist conservative who often cast the decisive vote on the high court, including to declare a right to same-sex marriage, uphold university affirmative action and preserve abortion rights.

Kavanaugh, who proved himself a far more conservative jurist on a lower appeals court for 12 years, could become the new key vote to begin dismantling Kennedy's social policy legacy.

But there was no talk of such consequences on Monday night. Rather, the 45-minute conversation at the Seventh Circuit bar and judicial conference touched on broader judicial themes, with friendly banter throughout.

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