Microwave heating technology is dependent on the dielectric properties of the materials being processed. The dielectric properties of H2SO4, H3PO4, ClSO3H, and H3CSO3H were investigated in this study using a vector network analyzer in an open-ended coaxial probe method at various temperatures. Phosphoric and sulfuric acids presented higher loss tangents in the frequency range 0.3-13 GHz, reflecting greater mobility of the ions and counterions. The acids were employed as catalysts in microwave-assisted homogeneous transesterification reactions for the production of methylic and ethylic biodiesel. The effects of catalyst concentration, alcohol to oil molar ratio, and irradiation time on biodiesel conversions were investigated. The results showed a significant reduction in the reaction time for microwave-assisted transesterification reactions as compared to times for conventional heating. Also, despite its higher loss tangent, it was observed that H3PO4 leads to lower conversion to biodiesel, which can be explained by its lower carbonyl protonation capacity.