SBR-1 EXPERIENCES ENCOUNTER WITH OPPOSITE DIRECTION TRAFFIC WHEN RADIO COMMUNICATIONS WITH CENTER ARE COMPROMISED.

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ON A NAVY TRAINING FLT FOR NAVIGATOR TRAINING AT FL240 WAS ASSIGNED A NEW FREQ/CTLR. WE TRIED NUMEROUS TIMES; (APPROX 5 OR 6) TO CHK-IN ON UHF FREQ; STUDENT AT LEAST TWICE; THEN I TURNED SQUELCH OFF; STUDENT TRIED AGAIN; THEN I TRIED TWICE. WE HEARD THE CTLR SAY OUR CALL SIGN 3 OR 4 TIMES. SHE WAS VERY BUSY ON VHF FREQ AND OUR CALL WAS FOLLOWED BY INSTRUCTIONS FOR ANOTHER ACFT. WE WERE TRYING TO REACH HER AND SHE WAS TRYING TO REACH US. THEN WE HEARD 'XXX (SHORT PAUSE; 1 SECOND MAX) CLB TO FL250.' I STARTED A SHALLOW CLB AND ALMOST IMMEDIATELY HAD A CONTACT ON TCAS (10 MI SCOPE) AT LESS THAN 1000 FT. I CLBED ABOUT 200-300 FT. WE HEARD THE CTLR TELLING SOMEONE TO TURN 180 DEGS; THERE WAS A CONTACT SHE WAS NOT TALKING TO AND I IMMEDIATELY STARTED A DSCNT TO FL240. SHE THEN TOLD THE CONTACT THEY COULD CONTINUE; THE OTHER CONTACT WAS CLR. SHE THEN CALLED; 'XXX;' THE STUDENT ANSWERED AT FL240 AND SHE ASKED US TO IDENT. WHEN WE LEFT HER SECTOR; SHE GAVE US A NUMBER TO CALL FOR A POSSIBLE 'FLT DEVIATION.' WHEN I LANDED; I CALLED THE NUMBER AND GAVE HIM THIS EXPLANATION. HE STATED THE 2 ACFT HAD NOT CLOSED INSIDE THE 5 MI BUBBLE AND THAT HE ANTICIPATED NO FURTHER INVESTIGATION. THE INSTRUCTOR FOR THE STUDENT NAVIGATOR TOLD ME LATER HE HAD THE XING TFC VISUALLY.