The full rare-earth (RE) chromites series (RE)CrO3 with an orthorhombic distorted (Pnma) perovskite structure and the isostructural compound YCrO3 can be synthesized through a simple microwave-assisted technique, yielding high-quality materials. Magnetization measurements evidence that the Neel temperature for antiferromagnetic Cr3+-Cr3+ ordering strongly depends on the RE3+ ionic radius (IOR), and a rich variety of different magnetic spin interactions exists. Dielectric spectroscopy on sintered pellets indicates electronic inhomogeneity in all samples as manifested by the presence of at least two dielectric relaxation processes associated with grain boundary and grain interior bulk contributions. X-ray diffraction, Raman spectroscopy, and temperature-dependent dielectric permittivity data do not indicate potential noncentroxymmetry in the crystal or concomitant ferroelectricity. Strong correlations between the magnetic and dielectric properties were not encountered, and microwave-synthesized (RE)CrO3 may not be classified as magnetoelectric or multiferroic materials.