A new two-standard calibration procedure is outlined for determining the complex permittivity of materials from the propagation constant measured with planar transmission lines. Once calibrated, a closed-form expression for the material permittivity is obtained. The effects of radiation and conductor losses are accounted for in the calibration. The multiline technique, combined with a recently proposed planar transmission-line configuration, is used to determine the line propagation constant. An uncertainty analysis is presented for the proposed calibration procedure that includes the uncertainties associated with the multiline technique. This allows line dimensions and calibration standards to be selected that minimize the total measurement uncertainty. The use of air and distilled water as calibration standards gives relatively small measurement uncertainty. Permittivity measurement results for five liquids, covering a wide permittivity range, agree very closely with expected values from 0.5–5 GHz.