Kara Swisher’s interviews made her famous among technology obsessives decades ago. She persuaded the rivals Bill Gates of Microsoft and Steve Jobs of Apple to play nice onstage. She reduced Meta’s founder Mark Zuckerberg, then just 26, to a puddle of sweat. She shoved her camera in the face of her future boss, Jim Bankoff, Vox Media’s chief executive, among others.

But it wasn’t until she began podcasting that she reached an audience far beyond the tech world.

In 2018, she started “Pivot,” a news-chat podcast, with Scott Galloway, a serial entrepreneur and marketing professor who now has his own slate of brash business podcasts under the name “Prof G.”

They were an odd couple — she was grouchy, he was raunchy — but their banter was tender and intellectual when they weren’t torturing each other. Fans began stopping Ms. Swisher in public, recognizing the aviator sunglasses that had become a swaggering signature.

“I’d never made a product or a news thing that people thanked me for,” Ms. Swisher, 62, said in a recent interview at a cafe in the shadow of the National Cathedral in Washington, where she lives with her wife and children. “At the end of this long career, it’s like, ‘Oh wow. I make something people really like.’”

So she and Mr. Galloway decided to assess its worth, shopping their portfolio of five podcasts around to other companies before their contract with Vox Media, their publisher, neared its end.

Competitive offers came in with guaranteed payments of about $40 million on four-year contracts, Ms. Swisher said. But in the end, they agreed to re-sign with Vox Media, with an unusual twist.