John Mayer dedicates song to 'patient' Katy Perry

(CNN) -- John Mayer's "Born and Raised" tour got started over the weekend at Milwaukee's Summerfest -- with a tribute to Katy Perry.

Although the on-again, off-again pair hinted in the spring that their coupling had come to an end, their recent PDA and matching Fourth of July outfits have suggested that they're at least on speaking terms.

That much became crystal clear on Saturday, when Mayer paused toward the end of his opening show in Milwaukee to tell the audience just how great his "Katy" has been.

According to Rolling Stone, Mayer dedicated the performance's final song, "A Face to Call Home," to "Katy, who's been my face to call home."

Perry, 28, and Mayer, 35, have been linked since last summer, and were soon opening up about their relationship in the press. Mayer said in January that he was "quite happy" dating the pop star, while she admitted to Vogue magazine in its July issue that she's still "madly in love" with the singer/songwriter, although she said at the time that their romance was done.

But Mayer didn't seem concerned with their relationship status on Saturday, when he opened up to the audience about his recovery from his 2012 throat surgery, during which Perry remained by his side.

"I was still getting to know this girl, and I wasn't going to be able to talk to her," Mayer recalled. "And she was more incredible than I ever thought. I would whisper in her ear, and she would order for me with the waiter, or I would whisper in her ear, and she would tell people, 'It's nice to meet you, he says.'"

He went on to describe a difficult courtship, crippled with a poor Internet connection and bad cell phone service, "and she was so patient to even continue to get to know me and love me," Mayer said. "This is a long time coming for the both of us, and I want to dedicate this next song to my Katy."