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Our recent discovery of magnetic fields in a small number of Herbig Ae/Bestars has required that we survey a much larger sample of stars. From our FORS1and ESPaDOnS surveys, we have acquired about 125 observations of some 70 starsin which no magnetic fields are detected. Using a Monte Carlo approach, we haveperformed statistical comparisons of the observed longitudinal fields and LSDStokes V profiles of these apparently non-magnetic stars with a variety offield models. This has allowed us to derive general upper limits on thepresence of dipolar fields in the sample, and to place realistic upper limitson undetected dipole fields which may be present in individual stars. Thispaper briefly reports the results of the statistical modeling, as well as fieldupper limits for individual stars of particular interest.

How non-magnetic are "non-magnetic" Herbig Ae/Be stars?