  We have obtained accurate circular spectropolarimetric observations for a
sample of Vega-like and Herbig Ae/Be stars with FORS1 at the VLT in an attempt
to detect their magnetic fields. No magnetic field could be diagnosed in any
Vega-like star. The most accurate determination of a magnetic field, at 2.6
sigma level, has been performed for the Vega-like star iota Cen for which we
have measured <B_z> = -77+-30 G. In the prototype of Vega-like stars, the star
beta Pictoris, which shows conspicuous signs of chromospheric activity, a
longitudinal magnetic field is measured only at ~1.5 sigma level. We diagnose
for the first time a longitudinal magnetic field at a level larger than 3 sigma
for the two Herbig Ae stars HD31648 and HD144432 and we confirm the previous
detection of a magnetic field in a third Herbig Ae star, HD139614. Finally, we
discuss the discovery of distinctive Zeeman features in the unusual Herbig Ae
star HD190073 where the Ca II doublet displays several components in both H and
K lines. From the measurement of circular polarization in all Balmer lines from
H_beta to H_8 we obtain <B_z> = +26+-34 G. However, using for the measurement
of circular polarization only the Ca II H and K lines, we are able to diagnose
a longitudinal magnetic field at 2.8 sigma level, <B_z> = +84+-30 G.
