My puppy ate cooked pork bones and is throwing up. What should I do?

Dogs will be dogs! As a veterinarian, I always recommend to my clients not to allow their pets to consume any cooked bones. As you have already intimated, these tend to break up into shards or splinters, leading to potentially disastrous consequences. It certainly sounds like the pork Sargent consumed is not agreeing with him in one way or another. Two episodes of vomiting by itself is not terribly many. However, if you note continuing vomiting throughout the next few hours, I would absolutely recommend seeking medical attention. In addition to a bone splintering and causing physical damage to the GI tract, theses types of foods have also been known to cause pancreatitis. The clinical signs of this condition will include lethargy, vomiting, and unwillingness to eat. Another thing to look out for over the course of the next several hours will be any blood in the feces. A small amount of blood in the feces is not very concerning, but any amounts of pooling red blood is a definite cause of immediate concern. If you do choose to take your dog to the vet, it is highly likely they will want to take some x-rays to see if it appears the bones are passing through the GI tract. They are also able to run blood work to determine if pancreatitis may be brewing. Should they determine things are looking OK, your vet may want to administer some medications to help calm the gastrointestinal system and prevent further vomiting.