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We have made a wideband measurement of the real part of the dielectric constant of flame retardant #4 epoxy (FR4), a common high-frequency printed-circuit-board insulator. We designed a novel test circuit, an electrically long parallel-coupled microstrip resonator, which was etched on a 0.014-in FR4 substrate, manufactured by NELCO, Melville, NY. We used a computer model of the resonator to extract the dielectric constant at the frequencies of zeroes in its measured transmission response. By adjusting the model's dielectric constant, we tuned the frequency of each zero to match the measured frequency, yielding the dielectric constant at that frequency. To validate our method and results, we present a simple, but original proof that the frequencies of zeroes in the resonator's transmission response are insensitive to input and output mismatches. Additionally, we compare the measured and predicted response of a two-stub filter designed with our measured data. The fabricated filter's measured return loss and insertion loss from 3 to 12 GHz are within 1% of the predictions of Agilent Technology's Momentum.