>>I don't think the US President actually holds in the air.<<
Nope, and Air Force One tools around at mach .92
Sometimes speed will be reduced a little enroute to meet an exact arrival time for protocol reasons.
Because AF1 has a military registration, diplomatic clearance must often be obtained by local U.S. embassies for oveflight of other countries even on regular airways. Also, AF1 sometimes can transit an FIR uncontrolled over the water by remaining outside territorial limits, the same principle used by VQ-1 and their EP-3's, and other military aircraft.
With heads of state in the third world, often a long, flowery, pro forma message of greetings is read on an ATC frequency when overflying friendly nations. "The Emir sends his greetings..." etc.