We obtained accurate circular spectropolarimetric observations of a sample of Vega-like and Herbig Ae/Be stars with FORS 1 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 , was performed for the Vega-like star \iota Cen , for which we measured \left < B _ { z } \right > = -77 \pm 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 \sim 1.5 \sigma level . We diagnosed a longitudinal magnetic field for the first time at a level higher than 3 \sigma for the two Herbig Ae stars HD 31648 and HD 144432 and confirm the existence of a previously detected magnetic field in a third Herbig Ae star , HD 139614 . Finally , we discuss the discovery of distinctive Zeeman features in the unusual Herbig Ae star HD 190073 , 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 \left < B _ { z } \right > = +26 \pm 34 G. However , using only the Ca ii H and K lines for the measurement of circular polarization , we are able to diagnose a longitudinal magnetic field at 2.8 \sigma level , \left < B _ { z } \right > = +84 \pm 30 G .