COMMUTER ACFT HAS ENG FIRE LIGHT ILLUMINATE ON CLB. UNABLE TO FIRE EXTINGUISHER BOTTLE. ENG SHUTDOWN. RETURN LAND.

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ON CLBING THROUGH 4000 FT AFTER DEPARTING MIAMI INTL; THE R FIRE INDICATION LIGHT ILLUMINATED. CAPT WAS FLYING AND CALLED FOR SHUTDOWN CHKLIST. WE CALLED ATC TO INSTRUCT THEM WE NEEDED TO RETURN TO MIA AND PROCEEDED TO SECURE ENG. WE FOLLOWED CHKLIST AS IN ACFT MANUAL SHUTDOWN PROC. STILL HAD INDICATION SO WE FIRED BOTTLE! IT DID NOT FIRE. AT THIS POINT THE CIRCUIT BREAKER FOR EXTINGUISHER POPPED; WE RESET IT AND TRIED AGAIN TO FIRE BOTTLE WITH NO LUCK. CIRCUIT BREAKER POPPED AGAIN. THE ENTIRE TIME WE KEPT MONITORING ENG VISUALLY AND IT APPEARED TO BE OK. NO FIRE! AT THIS POINT WE THOUGHT OF THE POSSIBILITIES OF AN INDICATION PROB; RATHER THAN ENG FIRE. AT ANY RATE WE ADVISED ATC THE NATURE OF PROB; THAT WE HAD FIRE INDICATION AND WE HAD SHUT DOWN ENG; NUMBER OF PAX/PERTINENT INFO. DECLARED EMER AND WERE RETURNING TO MIA. WE ADVISED PAX OF THE PROB; TOLD THEM WE THOUGHT IT WAS PROBABLY ONLY INDICATION PROB BUT IT WAS NECESSARY TO PROCEED BACK TO MIA TO LAND. WE AGAIN BRIEFED FOR EVAC PROCS ONLY ON OUR COMMAND TO EVAC IF INDEED FIRE. WE RETURNED FOR LNDG IN MIA WITH NO FURTHER INCIDENT AND LANDED SAFELY IN MIA! MAINT CONFIRMED ELECTRICAL INDICATION PROB.