What would cause your Saturn to sputter and then stall while driving with a half tank gas or less then run fine with a full tank?

I had a similar proplem , It turned out to be the fuel pump ( the fuel pump is cooled with the fuel in the tank as the tank went below half the pump would just stop causing the the car to die , after waiting for 30 minutes it would work again for a short time , Take your car to a garage they can test your pump for you.

And while they are looking at the fuel system, have them change the fuel filter, as the fuel tank maybe loaded with rust and crap, which is being pulled in by the fuel pump.

AnswerI had the same problem. I put a new fuel pump on the car and the problem seemed to be gone. About a week later it started again accept this time the car wouldn't even try to crank until it had cooled for about an hour. After many days of pulling out my hair i figured out that it was the crankshaft position sensor. I replaced the sensor for about $90 and now I'm good to go.