Currently with the ArcMap 10.0/1 service pack 4 and above, after an authorization a client machine loses the ability to print out its own ESU license.
This may be for security but it greatly hinders IT managers and support staff, as well as users when a situation occurs where a license may be damaged and IT cannot get to the machine. Under normal situations one could look up the ESU on the portal but the only field with identification is "Details", an optional field for entry. In our situation we have over 300 licenses and extensions so if one detail field is not filled out, we have no way of finding that ESU unless we deauthorize that machine. In situations where this machine is sent to a field team, or in a secure environment we cannot get back into we now have to cross check dates to see which machine was authorized on that date to even begin a recovery. Truthfully better record keeping will avoid this issue but as it stands in the predicament we are in now, there is no way to recover unless more than 40 machines across the world are deauthorized and reauthorized.
With ArcGIS 9.3/10 SP 1 you could write a script to return an ESU/EFL, or manually locate it. Now you are out of luck and hindered. Please look into a way of bringing this back.