try to raise ARINC on HF

I believe my answer, climb to MSA, go to Missed Approach holding point, satisfies both.

This is actually a good question, all joking aside. Me personally, climb to MSA while still on arc as best as possible (engaging climb mode and continuing 5 degree heading cuts to maintain the arc for another 5 minutes ain't gonna kill anybody while you climb to MSA), then proceed to the holding pattern and obtain ATC clearance.

making a hard bank to the station the nanosecond I loose DME? Nah don't know about that one....

All joking aside, this dead reckoning around the arc as you climb to the MSA appears to me be the best answer assuming your hands are as tied as others have suggested - no ATC, no radar, no other equipment (official or not). Even in an aircraft with poor climb capability (the issue I have with Tony's answer), this will probably keep you from hitting something as you get up there (including the mountain between the arc and the MAHF).

The one thing I did not see in these answers is to make the mandatory call to ATC of "Missed Approach".

I agree with dead reckoning the arc while climbing to MSA (which may be higher than missed approach altitude), and then flying the approach path to the missed approach point while trying to contact ATC for a different clearance.

Joe

The only problem I have with Noy's (sensible) solution is that a situation as common or possible as this one would seem to merit a specific procedure of some kind. Since aircraft performance would be known factor in this scenario, it seems like a company ops manual would address it. So at an interview I would give that as my primary response, and if the interviewer replies there is no company solution, THEN I would ask if we could get back to MSA and how fast we could get there.

I wouldn't over think the question too much for an interview. They just want to know what you would do to keep the airplane intact and satisfy regulatory requirements. I wouldn't be pulling out sectional charts, your handheld GPS, Ipad or any of that silly BS. Just fly the airplane.

This is the best answer.

So wait, did we just lose the DME, or the VOR and DME?

Required obstruction clearance (ROC) along the arc
depends on the approach segment. For an initial
approach segment, a ROC of 1,000 feet is required in
the primary area, which extends to 4 NM on either side
of the arc. For an intermediate segment primary area
the ROC is 500 feet. The initial and intermediate segment
secondary areas extend 2 NM from the primary
boundary area edge. The ROC starts at the primary
area boundary edge at 500 feet and tapers to zero feet at
the secondary area outer edge.

The total width of an arc intermediate
segment is 6 NM on each side of the arc. For obstacle
clearance purposes, this width is divided into a primary
and a secondary area. The primary area extends 4 NM
laterally on each side of the arc segment. The secondary
areas extend 2 NM laterally on each side of the primary area.

So let's say you're flying the arc at 150kts...2.5 miles/min. I'd say "dead reckoning" for a few moments to begin the climb and reconfigure is your best bet. Just figured it would be good to see the obstacle clearance figures. Although, I can't say what the obstacle clearance limits are in other parts of the world. Don't forget to check the approach chart for your highest obstacles in the area either!