That's exactly what happened to Nikki Bumatay and her fiancé when they recently ran into the singers while hiking at Fryman Canyon Park in Studio City, Calif.
"We were sitting in our car when this Maserati pulls up...I look back and see who gets out of the passenger door and it's Selena Gomez," Bumatay told PEOPLE.
But that wasn't what excited her the most!
"I look at the person who squeezes out of the driver side door [and] realize it's Katy Perry, my absolute biggest girl crush," she added.
How awesome would it be to run into Katy and Selena like that?
So, who did the fan think was the coolest of the two celebs?
She said Katy wore "shiny pink lip gloss" and was "very goofy and extremely gracious." As for Selena, she was a little more reserved.
Maybe Selena and Katy were going on a hike to talk about their latest breakups? We'd love to hear those deets!
Have you ever randomly ran into a celeb? Let us know!