My specialty at ZAB has a large swath of airspace ready to protect in case the shuttle needs to land at White Sands.
*Opening the LOA that I really should have memorized by now...*
Disclaimer: I am going to assume my LOA between ZAB and NASA is for official use only, so... I'm not going to divulge specific information for national security reasons.
Basically, ZAB is notified ahead of time when and where the space shuttle will be entering their airspace. Traffic would need to be routed around to protect the airspace the shuttle would be using from the top of Class A airspace to the ground.
Since the shuttle is a glider, ATC wouldn't be able to give any sort of really meaningful clearance. That, and with re-entry procedures being as complex as they are, the shuttle would most certainly need to maintain contact with NASA through and after the touchdown and rollout. They have such intensive telemetry, they could tell the shuttle much, much more quickly of any observed deviations from the flight path.
I know there are people much more knowledgeable about these things than I (FC?), but there was never any talk of actually speaking to the shuttle when there was a possibility of a divert to white sands a few months back. Just excitement of seeing a blip hop across the scope a few inches at a time (really really fast).
~Nate