A precision microwave effective linewidth measurement technique for magnetic samples has been developed. The measurement utilizes a high-Q cylindrical cavity that contains the sample of interest, a highly stable and programable static magnetic field source, a computer controlled network analyzer for cavity center frequency omega c and quality factor Qc determinations, and the standard metrological substitution ABA method for accurate relative omega c and Qc measurements. Sequential long term ABA measurements show that the time and temperature drifts and random errors are the dominant sources of error, with uncertainties in omega c/2pi and Qc in the range of 50 kHz and 25, respectively. The ABA method is applied to eliminate these drifts and minimize the random errors. For measurements over 25 ABA cycles, accuracy is improved to 0.14 kHz for omega c/2pi and 3 for Qc. The temperature variation over a single ABA cycle is generally on the order of 10(-3)-10(-5) degrees C and there is no need for any further temperature stabilization or correction measures. The overall uncertainty in the 10 GHz effective linewidth determinations for a 3 mm diam, 0.5 mm thick polycrystalline yttrium iron garnet (YIG) disk is 0.15 Oe or less, well below the intrinsic single crystal YIG linewidth. This represents a factor of 10 improvement in measurement accuracy over previous work.