You could hire another Cessna to pursue to its home airport. If it goes in circles it might be possible to launch when it looks like it is leaving the region, and you can figure out the endurance and range using published data. It may be an FBI plane doing some a mission (be careful). Before doing a recon mission I would try to find out if it is them, maybe let the FAA know what you plan to do first, and see if that gets a response from anyone.
[mod note] this belongs in Hangar Talk for now.