A parallelogram-shaped hysteresis loop is chosen to represent the flux response of a material subjected to sinusoidally varying magnetic field excitation. For excitation frequencies exceeding 100 MHz, a precise measurement of the loop shape is often impractical because of the limited bandwidth and accuracy of the measuring instruments. To simulate the effect of low-pass filtering, Fourier coefficients are computed analytically and a hysteresis loop is then reconstructed from one or more of the lowest-order harmonics. The analysis shows that it is sufficient to measure just a few harmonics to obtain an excellent approximation of the exact hysteresis loop shape. Measurement of the harmonic content of the response by means of a spectrum analyzer is suggested for determining how many harmonics are needed to achieve a desired precision in the hysteresis loop shape. We also emphasize that for purely sinusoidal excitation, power dissipation is given directly, regardless of the hysteresis loop shape, by just the quadrature at the fundamental frequency component of the response waveform. Thus dissipation mechanisms which degrade the permeance at high frequency and at large flux-amplitude can be conveniently measured with a network analyzer.