My 3 year old Cane Corso swallowed three pork rib bones yesterday and threw up this morning. I don't think he chewed them; I was turned away and didn't hear any crunching but am nevertheless concerned. He's pooped since and eaten normally but I'm not sure if this isn't the "calm before the storm." Advice?

My advice is to ask your Vet - I'm sure a Vet Tech or two will come on with advice, but I don't know how long that will take.

You should call your vet first and foremost.
Bones do have the potential to cause some pretty serious issues. They can cause lacerations in the intestinal tract, impactions and blockages along the digestive tract.
The things to look for will be vomiting, dry heaving, blood from the rectum, painful abdomen lack of appetite.
I've seen dogs pass some pretty strange things, but don't count on it.
Better safe than sorry, I'd get him checked out.