FLC OF A LEAR JET 36 LOST COMS DURING HIGH ALT AFTER DEP FROM ANCHORAGE PRIOR TO REACHING THEIR FLT PLAN REQUESTED ALT. THEREFORE; AFTER APPROX 20 MINS OF TRYING TO CONTACT THEM THEY CLBED TO THEIR FILED ENRTE ALT. THEY SUBSEQUENTLY RECEIVED CONFIRMATION OF THEIR REQUESTED ALT THROUGH ANOTHER ARTCC CTR.

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AFTER DEP FROM COLD BAY; AK; WE WERE GIVEN FL290 AND EXPECT HIGHER AFTER RADAR CONTACT. AFTER ZAN CONFIRMED THEY HAD RADAR CONTACT; WE WERE GIVEN FL330. 10 MINS LATER ZAN CALLED US BUT DID NOT HEAR OUR REPLIES. WE ATTEMPTED TO CONTACT ZAN ON 118.5 AND 132.9 AT LEAST 20 TIMES OVER THE NEXT 10-20 MINS. WE ALSO ATTEMPTED A NUMBER OF HF FREQS WITH NO LUCK. AFTER ASSUMING A LOST COM SIT; WE DECIDED WE SHOULD CLB TO OUR FILED ALT OF FL370. WE WERE GIVEN THE INITIAL CLRNC OF FL290; EXPECT HIGHER AFTER RADAR CONTACT. WE WERE IN RADAR CONTACT AT LAST COM AND HAD FILED FOR FL370. WE CALCULATED THAT WE WOULD BE BELOW MINIMUM FUEL IF WE MAINTAINED FL330 WHICH ALSO INFLUENCED OUR DECISION TO CLB TO FL370. WE HAVE TRIED TO FIGURE OUT HOW TO AVOID THIS SIT FROM RECURRING; BUT THINK WE FOLLOWED THE PROPER PROCS AND HOPE THAT WE CAN FIND AN ACTIVE FREQ A LITTLE QUICKER NEXT TIME TO AVOID ANY UNCERTAINTIES. WE EVENTUALLY CONTACTED HNL RADIO ON 113.30 AND; AFTER HNL SPOKE WITH ZOA; WE WERE CLRED TO MAINTAIN FL370.