The hurdles of running a contemporary-art museum in the West African country of Benin might seem light years away from the concerns of the Metropolitan Museum of Art, one of the world’s largest and wealthiest.

But some issues span continents, affecting institutions big and small—how to connect with audiences, for example, in an increasingly digital world.

The Met in April is hosting a meeting of museum leaders from 15 countries to talk shop, compare notes on management and forge new ties with peers from other parts of the world.