His show, and Mr. Colbert’s show, will “need to work out what we become next,” Mr. Oliver said.

These alumni of “The Daily Show,” Comedy Central’s long-running news satire, find themselves at different places in their professional trajectories. Mr. Oliver has enjoyed widespread critical praise for “Last Week Tonight,” a weekly half-hour show that recently won the Emmy Award for outstanding variety talk series.

Mr. Colbert, who was largely invincible when he played a fake conservative pundit on “The Colbert Report,” is trying to strike the right tone on “The Late Show,” an hourlong network talk show that runs five nights a week. He is coming off a live election-night special, broadcast on Showtime, that became increasingly surreal and funereal as the program wore on.

(On Saturday, Mr. Colbert said little about this special, except to mention that his staff had hired a team of male models, with the slogan “I’m with her” painted across their rear ends, in the event that Mrs. Clinton won. “And then very early on the evening, we were like, ‘You can let those guys go,’” he said.)

Mr. Oliver said that it had not been much fun to write jokes about the brutal presidential campaign.

Usually in his line of work, he said: “You try and take things of substance and then put some sugar on it to make it palatable. But there was so little of substance, this whole campaign, it’s just like a diabetes-inducing amount of sugar. Your job kind of flips on its head.”

Somewhat facetiously, Mr. Oliver, who is a British citizen, talked about whether his frequent comedic jabs at Mr. Trump might mean that he now has to return to his home country.