Enroute Controller described an emergency event experienced by a military aircraft; the event hampered due to lack of both needed land lines to adjacent Approach Control facilities and UHF frequencies.

Narrative

An F15 was doing supersonic speed run; the flight was on RVSM; and up at 430B550; when almost finished with the run pilot called and said something that couldn't quite be heard because an aircraft checked in. So we ask for them to repeat. The aircraft called back and declared an emergency and said he was going direct [to his] destination. I got on the line with the sector below us after PVD'ing the aircraft to them and advised that the F15 had declared and emergency and was going direct to his destination. The R-Side had told the aircraft to descend and maintain FL360 and was trying to get a response from the pilot. I PVD'd the aircraft to the lowest sector in our area and called to advise of the emergency. Sometime during these coordination's the pilot advised that they had an engine fire and they where at or leaving FL230 and the supervisor was called. He was military and on UHF but because we were in the ultra high sector we didn't have access to the Military Approach UHF or the line to Military Approach so I could call and coordinate with about the emergency. We need Military Approach UHF frequencies to give to the pilot but we didn't have access to them or a line to the Military Approach on our sector.