Is there a way to wait till the receiving party processes message sent using port.postMessage(message)? I'd expect something like callback passed as second argument similarly to chrome.scripting.executeScript(injection, callback)
To my knowledge not natively but a wrapper is easy to implement. You need a class that will generate a random UID (Unique ID) for each message and store a map { [uid]: cb }. Attach generated UID to the message. Response will also need to contain same UID.