Herbig Ae/Be (HAeBe) stars are pre-main sequence objects of moderate mass representing the early evolutionary stages of β Pic-type stars. The objects of both kinds are surrounded by dust disks/shells, and the dust is believed to be continually replenished by comet-like bodies orbiting close to the stars. As the dust particles in the β Pictoris disk are likely to be as fluffy as cometary dust is, it is reasonable to suppose that the grains around HAeBe stars could be porous as well. This brings up the question, which we try to answer here, of how the grain porosity affects the observational manifestations of the dust shells of HAeBe stars: the excess infrared emission, anomalous extinction in the ultraviolet, and the peculiar behavior of color indices and linear polarization during deep brightness minima observed for about 25% of HAeBe stars (UX Ori, WW Vul, etc). We have performed numerical Monte Carlo simulations of polarized radiation transfer in spheroidal inhomogeneous shells for three different models of circumstellar dust grains. In addition to the observational data mentioned above, intensity scans and polarization maps of the objects have been constructed in view of possible future observations. It is found that the porosity of circumstellar grains weakly affects the spectral energy distribution (when the grain model does not include particles with quite different optical properties) and does not show pronounced effects in the intensity and polarization maps for all grain models considered. On the other hand, the porosity normally reduces single-scattering albedo of particles, and therefore, fluffy grains explain the spectral energy distributions of UX Ori-like stars and their tracks in the color-magnitude diagrams considered in combination much better than compact grains do. However, highly porous, cometary-like grains are unlikely to be abundant in the shells as they produce too low linear polarization to account for the observations of the HAeBe stars.