There isn't a nice way and it doesn't seem to be a good idea to do this. Your frontend should call your backend not the other way. So the easiest way to do this would be to store the errors inside your service and have your page get these.
class MyService {
private String error;
public void doBackEndThing(){
try {
backEndService.doRemoteCall();
} catch (BackendException e) {
error ="Backend is currently not available";
}
}
}
and
class MyPage extends WebPage {
private MySerivce service;
public void doSomethingFrontendy() {
error = service.getError();
}
}
or you could return an error from your backend method or throw an Exception and handle this in your WebPage or use IRequestCycleListener#onException() like @svenmeier pointed out.