Any way for React in a popup to communicate with parent window?

Eelke's suggestion was spot on.

I used window.postMessage() in the child window, then window.close(), then added a window.addEventListener('message', function(){}) in the componentDidMount method of of main/master component.

Check out https://facebook.github.io/react/tips/dom-event-listeners.html for more information!

When you are unable to establish any parent-child or sibling relationship between the components, React recommends setting up an event system.

For communication between two components that don't have a parent-child relationship, you can set up your own global event system. Subscribe to events in componentDidMount(), unsubscribe in componentWillUnmount(), and call setState() when you receive an event. Flux pattern is one of the possible ways to arrange this.

see https://facebook.github.io/react/tips/communicate-between-components.html

Have a look at window.postMessage for cross window communication (https://developer.mozilla.org/en-US/docs/Web/API/Window/postMessage)