Among the 21 Herbig Ae/Be stars studied, new detections of a magnetic field were achieved in six stars. For three Herbig Ae/Be stars, we confirm previous magnetic field detections. The largest longitudinal magnetic field, <B_z> = -454+-42G, was detected in the Herbig Ae/Be star HD101412 using hydrogen lines. No field detection at a significance level of 3sigma was achieved in stars with debris disks. Our study does not indicate any correlation of the strength of the longitudinal magnetic field with disk orientation, disk geometry, or the presence of a companion. We also do not see any simple dependence on the mass-accretion rate. However, it is likely that the range of observed field values qualitatively supports the expectations from magnetospheric accretion models giving support for dipole-like field geometries. Both the magnetic field strength and the X-ray emission show hints for a decline with age in the range of ~2-14Myrs probed by our sample supporting a dynamo mechanism that decays with age. However, our study of rotation does not show any obvious trend of the strength of the longitudinal magnetic field with rotation period. Furthermore, the stars seem to obey the universal power-law relation between magnetic flux and X-ray luminosity established for the Sun and main-sequence active dwarf stars.