I know I'm extremely late to the party, but since I've encountered a similar roadblock recently, I'll share my own findings, with a hope it will help someone facing a similar issue in the future.
If you want some sort of "global" handling, in order to, for example, display error messages to the user, you can do as I did - but this is by no means a perfect solution.
Let's suppose your MyGame class extends Game or implements ApplicationListener. If that's the case, you can override its create(), render() methods and so on. If you do not use the main class, you can override these methods like so:
@Override
public void render() {
try {
super.render();
} catch (Exception e) {
handleError(e);
}
}
You can do the same to other methods, such as create(), pause(), resume(). This ensures that when an exception is thrown somewhere, the MyGame object will be able to intercept it.
Treat my handleError(e) as a placeholder for what you actually want to do. You can use some platform dependent error display - for example, you can use Swing on desktop, but something else for Android.
Also, you might want to ensure everything gets disposed properly when you handle an exception and have the program terminate as a result.