With an English curb bit, twist the chain toward the horse's chest until it lies flat. Sharp points where the mouthpiece is attached to the shanks can bother the horse. When fitting a curb, it should fit right in the corner of the lips, not be pulled up tight. You also want to make sure the mouthpiece fits. Too wide and it will rock from side to side in the mouth.
Balance also plays a role.
If your horse is throwing his head up when you're stopping, look to yourself first. Make sure you're using your hands properly. Then make sure that the bit is adjusted properly and that it is the right bit for the horse. Before you stop a horse in a curb bit, let him know your intentions. Pick up the reins gently so your horse feels it and gets ready.