GLF4 CREW HAD AN ALT OVERSHOT WHILE ON A GAR AT RWY 19 AT TEB.

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ON ARR TO TETERBORO; NJ; CLRED FOR ILS RWY 19 WITH GS INOP. SET UP FOR LOC ONLY RWY 19 APCH. ON EXECUTION OF THE MISSED APCH; 1500 FT WAS SET IN THE ALT PRESELECT. PF PRESSED GAR ON THE AUTOTHROTTLES; WHICH SET GAR EPR; AND COMMAND BARS DISPLAYED A 12 DEG NOSE UP CLB. I SELECTED FLAPS 20 DEGS; GEAR UP; HDG 205 DEGS; AND FLT LEVEL CHANGE. COMMAND BARS DISPLAYED 12 DEG NOSE UP. ACFT CLB RATE WAS APPROX 3000-4000 FPM. ALT SELECT DID NOT CAPTURE. PF WAS STOPPING THE CLB; BUT AT THAT RATE OF CLB; WAS UNABLE TO STOP IT BY 1500 FT; AND APCHING 3000 FT; EXCEEDING MISSED APCH ALT; LEVELED OFF. ATC ADVISED US THAT WE CAME CLOSE TO ANOTHER ACFT ON APCH TO NEWARK. WE WERE GIVEN RADAR VECTORS FOR ANOTHER APCH TO RWY 19; GS INOP. THIS APCH ENDED IN A MISSED APCH. AWARE THIS TIME THAT ALT DID NOT CAPTURE BEFORE; AUTOTHROTTLES WERE NOT USED; AND A GRADUAL CLB TO WAS MADE 1500 FT. ALT HOLD CAME ON. ATC VECTORED US FOR ILS RWY 6; WHICH ENDED IN A LNDG. A MAINT ITEM WAS ENTERED; AND A CONVERSATION WITH HONEYWELL REVEALED THAT WITH THE MDA OF 580 FT AND ALT OF 1500 FT; THE ALT SELECT MAY NOT CAPTURE WITH SUCH A HIGH CLB RATE. SUPPLEMENTAL INFO FROM ACN 578043: I WAS FLYING L SEAT. AN AUTOTHROTTLE ASSISTED MISSED APCH WAS INITIATED. THE ALT GUIDANCE DID NOT CAPTURE THE PRESELECTED MISSED APCH ALT. THEY HAVE RESEARCHED HONEYWELL MANUALS AND QUERIED HONEYWELL REPRESENTATIVES. ACCORDING TO BOTH SOURCES; THE ALT GUIDANCE MODE; PRESELECT; MAY OR MAY NOT CAPTURE CERTAIN OUTSIDE PARAMETERS.