Natasha Grano and Michael Graziano said their intimate wedding with four guests on June 5 was “elegant and powerful.” Equally special was the ceremony a day after, attended by thousands on the social media app Clubhouse, where their closest confidants gather.

The two probably wouldn’t have even met had Ms. Grano not fallen in love with the sound of Mr. Graziano’s voice on the audio-only platform that bears some resemblance to an old-fashioned party line.