If communications failure happens in VMC, or if VFR conditions are encountered after the failure and you can stay in VMC, you should continue the flight under VFR and land as soon as practicable
If the failure occurs in IFR conditions, then you should continue your flight, and ATC will also assume that you are continuing, and clear airspace accordingly. The three elements of the navigation are:
Route
Altitude
Leaving the clearance limit in order to shoot the approach
ROUTE
as Assigned
as Vectored
as Expected
as Filed.
1. Assigned: Fly the route assigned in the last ATC clearance received.
2. Vectored: If being radar vectored, fly directly to the fix, route, or airway specified in the vectoring clearance.
3. Expected: In the absence of an assigned route, fly the route that ATC told you to expect (in a further clearance).
4. Filed: In the absence of an assigned or expected routing, fly what you filed in your flight plan.
ALTITUDE
Fly the highest of these three, for the segment of flight you're on:
Assigned Altitude
Expected Altitude
MEA
Plan to leave the clearance limit or the IAF (if the limit was the airport itself) at the time calculated from your flight plan. On the plan was an expected time enroute: add that to your departure time off, and start your instrument approach procedure at that time. If you arrive at the clearance limit before then, hold there until that expected arrival time.