But he didn’t have to. “She came up and said ‘Hey Ross!’,” Mr. Girard said. “She had been reading all of Alex’s posts. She didn’t even need to ask my name.”

Mr. Goldschmidt and Mr. Girard don’t consider “King of My Heart” their song, the one they fell in love to. Instead, “it was a song that had always resonated with me and my own story, because it’s about someone who has become content with being alone and getting to that place of self love, and then suddenly having someone come into their life and rock their world,” Mr. Goldschmidt said.

He didn’t beg, cajole or even ask Ms. Swift to sing it at the surprise engagement party he had been planning for months. Instead, Ms. Swift’s publicist, Tree Paine, reached out to him.

“I had sent Taylor an email thanking her for all of the years of advice on love and on life and for that song, which had sunk into my heart,” Mr. Goldschmidt said. Two weeks later, Ms. Paine called to say Ms. Swift would like to be part of their engagement day.

It isn’t the first time Ms. Swift has surprised a couple. In June 2016, she crashed the wedding of Max Singer and Kenya Smith, and about 100 guests in Long Beach Island, N.J., before sitting down at a piano and performing her hit song “Blank Space.” Other couples have been sent champagne and she’s shown up at bridal showers.

Mr. Goldschmidt was driving to work in late January when he got the call. “Basically, I lost feeling in my face and I had to pull my car over,” he said. “I cried a little bit, I screamed a little bit, then I tried to restore the feeling to my face.”