In this work, we present a new X-band waveguide (WR90) measurement method that permits the broadband characterization of the complex permittivity for low dielectric loss tangent material specimens with improved accuracy. An electrically long polypropylene specimen that partially fills the cross-section is inserted into the waveguide and the transmitted scattering parameter (S21) is measured. The extraction method relies on computational electromagnetic simulations, coupled with a genetic algorithm, to match the experimental S21 measurement. The sensitivity of the technique to sample length was explored by simulating specimen lengths from 2.54 to 15.24 cm, in 2.54 cm increments. Analysis of our simulated data predicts the technique will have the sensitivity to measure loss tangent values on the order of 10(-3) for materials such as polymers with relatively low real permittivity values. The ability to accurately characterize low-loss dielectric material specimens of polypropylene is demonstrated experimentally. The method was validated by excellent agreement with a free-space focused-beam system measurement of a polypropylene sheet. This technique provides the material measurement community with the ability to accurately extract material properties of low-loss material specimen over the entire X-band range. This technique could easily be extended to other frequency bands.