ZSU Controller voiced concern regarding the lack of communications coverage utilizing a supervisory selected back-up frequency during a primary frequency outage that resulted in a possible airspace/procedural infraction.

Narrative

I relieved R4 and the Controller told me that an A340 needed some route amendment which I gave to the pilot including a crossing restriction for his climb towards the SOCCO Intersection. The read-back for the clearance was complete and correct and the pilot also advised that he was going to comply with the altitude crossing restriction. The restriction was to cross 10 miles from the SOCCO Intersection at and maintaining FL370 and if he was unable to advice. To the best of my knowledge the pilot did not comply with the restriction. The main problem with this situation was that I was using a frequency that has no coverage to the northeast of our airspace but this frequency was assigned by management earlier during the day for the sector. The main frequency for the sector; 125.0; was called out of service earlier. The frequency 124.22 is a frequency that is used as a backup frequency for the R6 Sector which is adjacent with ZMA Center to the northwest of our airspace. I believe the pilot tried to communicate that he was not going to be able to make his restriction because I heard some noises on the receiver for 124.22 but no voice. Then I tried to reach the pilot but got no response at all. By this time it was too late to even let ZNY Center know that the aircraft was not going to be leveled by the boundary at SOCCO. The aircraft progressed the boundary climbing from about FL366 climbing to FL370; and leveled of at FL370 approximately 6 miles north of the boundary according to the aircraft data block. At this time there were no other aircraft in the vicinity of the SOCCO Intersection that could have been a problem for the aircraft. Again; the pilot could have tried to let me know that he was leveled at FL370; but since the frequencies were not working properly; and the lag of data presentation on my scope; the pilot could have very well made his restriction and I did not know due to the frequency problem. The supervisors should select a frequency that has proper coverage for the airspace in question; even if it means using frequencies from adjacent sectors to R4.