Update, native promises now do the following in most browsers:

window.addEventListener("unhandledrejection", function(promiseRejectionEvent) { 
    // handle error here, for example log   
});

We were just discussing this the other day.

Here is how you’d do this with bluebird:

window.onpossiblyunhandledexception = function(){
    window.onerror.apply(this, arguments); // call
}

window.onerror = function(err){
    console.log(err); // logs all errors
}

With Bluebird it’s also possible to use Promise.onPossiblyUnhandledRejection. The calls for done are not needed as the library will detect unhandled rejection itself unlike Q (UPDATE 2016 – I now wrote code for Q and it does this).

As for native promises – they will eventually report to either window.onerror or a new handler but the specification process is not yet done – you can follow it here.