AN EMB 135 CAPT RPTED THAT A NUMBER OF FACTORS CAUSED HIM TO OVERSHOOT HIS ALT DURING A MAP AT TEB.

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WE SHOT THE LOC RWY 19 APCH AT TEB. WE HAD TO EXECUTE A MISSED APCH DUE TO POOR VISIBILITY. DURING THE MISSED APCH; I LEVELED THE ACFT AT 1500 FT AND IMMEDIATELY TURNED THE AUTOPLT ON. I THEN CALLED FOR THE CHKLIST. AS I WAS MANEUVERING FOR THE MISSED APCH; MY CO-PLT CALLED 'ALTITUDE.' I NOTICED THAT THE ACFT WAS CLBING RAPIDLY AND MANUALLY ATTEMPTED TO ARREST THE ASCENT AND RETURN TO OUR ASSIGNED ALTITUDE. DURING OUR ALTITUDE DEVIATION WE GOT A 'TA' AND THEN AN 'RA' TO DESCEND. SHORTLY AFTER THIS TIME; THE CTLR ASSIGNED US A NEW HDG AND AN ALT OF 2000 FT; WHICH WE COMPLIED WITH. I THINK THE MAIN CAUSE OF THIS ALT DEV WAS THE AUTOPLT'S INABILITY TO TRIM THE NOSE DOWN FAST ENOUGH TO KEEP UP WITH OUR INCREASING SPD AFTER THE LEVEL OFF. THIS CAUSED THE ALT HOLD TO KICK OFF AND THE ALT DEV AS A RESULT. THIS COULD HAVE BEEN PREVENTED BY MANUALLY TRIMMING THE PITCH AS OUR SPD INCREASED BEFORE TURNING THE AUTOPLT ON. OTHER CONTRIBUTING FACTORS WERE THAT BOTH FLT CREW MEMBERS WERE RELATIVELY NEW TO THE ACFT TYPE; IT WAS LATE AT NIGHT; THE CREW WAS TIRED; THE WEATHER WAS POOR; AND WE HAD A FALSE GPWS ALERT.