Marketing and communications professionals are taking advantage of cost-effective digital and social media tactics, such as livestreaming and contests, to help brands get the most out of events they produce or sponsor.

On Monday, the Metropolitan Museum of Art in New York livestreamed the red-carpet arrivals at its swanky Costume Institute Benefit for the first time. The Met, Vogue, and Amazon.com, the event's lead corporate sponsor, collaborated to produce the live stream.

For Amazon.com, livestreaming the arrival of stars such ...