THE BRANIFF AND UNITED BOEING 727 JETLINERS WERE APPROACHING 'SWAPP' INTERSECTION ON CONVERGING JETWAYS AT THEIR PROPER ASSIGNED ALT OF 35,000'. THE CONTROLLER WAS IN THE PROCESS OF ISSUING RADAR VECTORS TO ASSURE PROPER LATERAL SEPARATION WHEN THE CONTROL FREQ BECAME BLOCKED. ATTEMPTS TO OVERRIDE THE BLOCKED FREQ WERE UNSUCCESSFUL AND THE TWO ACFT PASSED WITH APPROX 200' VERT AND ZERO HORZ SEPARATION. THE TWO FLT CREWS DID NOT SEE THE OTHER ACFT UNTIL THE NEAR COLLISION OCCURRED. THE INITIAL TRANSMISSION BY THE BRANIFF CAPTAIN FOLLOWING THE INCIDENT CLEARED THE FREQ AND ALL COMMS RETURNED TO NORMAL. BOTH ACFT LANDED WITHOUT FURTHER INCIDENT. THE FLT DATA RECORDER IN THE BRANIFF 727 INDICATED A SOLID 5 MINUTE EVENT MARKER OF MIC 'ON' THAT CORRELATED TO THE TIME OF THE INCIDENT. THE BRANIFF CREW WAS NOT AWARE OF THE FREQUENCY PROBLEM. THERE WERE NO DISCREPANCIES REVEALED DURING BENCH TESTS PERFORMED ON THE EQUIPMENT INSTALLED IN THE BRANIFF ACFT.