To build a beyond state of the art NSE spectrometer with a resolution tau>1 ms the spectrometer has to be equipped with superconducting (SC) precession coils for field integrals J>1Tm. A SC test system has been installed to asses the effects of flux trapping, "hysteresis" field etc. on the field integral and to study the magnetic field in time and space. Within a simplified model we were able to describe the field integral contribution of the `hysteresis' field quite sufficiently. An operational mode for superconducting coils to avoid any trapped flux by heating and subsequently cooling below Tc yields a magnetic field reproducibility of at least DB=8x10**(-6).