We report on conductance fluctuations of ballistic quantum dots in a strictly parallel magnetic field B. The quantum dots are patterned in two-dimensional electron gases (2DEG's), confined to 15- and 45-nm-thick GaAs quantum wells (QW) with one and two occupied subbands at B=0, respectively. For both dots we observe universal conductance fluctuations (UCF's) and, in the case of the wide QW dot, a reduction in their amplitude at large B. Our data suggest that the finite thickness of the 2DEG and the orbital effect are responsible for the parallel B-induced UCF's.