ACR X HAD LTSS FROM Y BECAUSE OF STUCK MIKE. SYS ERROR.

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ENRTE BTWN MAW AND VUZ VORS. CLR SKY; LEVEL AT FL370. LAST CLRNC: 'FLY HDG 140 DEGS UNTIL RECEIVING VULCAN; THEN PROCEED DIRECT.' WORKING WITH ZME ON 118.62. ACR X EXPERIENCED SEVERAL MINS DURING WHICH IT APPEARED THAT THERE WAS A 'STUCK MIKE' ON THE FREQ. ALL XMISSIONS ON THE FREQ WERE GARBLED AND TOTALLY UNREADABLE. WE ELECTED TO TRY TO RE-ESTABLISH CONTACT WITH ZME ON ANOTHER FREQ SELECTED FROM THE HIGH ALT ENRTE CHART. THE FIRST FREQ RESULTED IN CONTACT WITH NASHVILLE APCH; WHO DIRECTED US TO ZTL; WHO THEN PASSED US ON TO A CORRECT FREQ FOR ZME. BTWN EACH OF THESE FREQ CHANGES; WE RESELECTED 118.62 AND CONTINUED TO FIND THE 'STUCK MIKE' SIT EXISTING. AS WE WERE RE-ESTABLISHING CONTACT WITH ZME (127.37) WE RECEIVED A TCASII ALERT (TA) AND OBSERVED AN ACFT Y AT OUR ALT PASS OUR NOSE FROM R TO L ABOUT 3-4 MI AWAY. ZME TOLD US TO TURN TO HDG 180 DEGS. WE STARTED THE TURN AND ADVISED ZME WE HAD THE TFC IN VISUAL CONTACT. ZME CLRED US BACK ON FLT PLAN. A POTENTIALLY HAZARDOUS SIT WAS PRESENTED BECAUSE THERE IS NO PROC FOR RE-ESTABLISHING CONTACT WITH ATC DURING A 'STUCK MIKE' SIT. BACKUP FREQS COULD BE PUBLISHED ON THE ENRTE CHARTS (IE; 118.62 (127.37)) -- INDICATING IF A PROB DEVELOPS ON 118.62 ATTEMPT CONTACT ON 127.37. ALSO CHK HIGH ALT CHART TO ASSURE FREQS GIVEN ARE VALID.