We develop a Monte Carlo technique to test models for the true power spectra of intermittently sampled light curves against the noisy, observed power spectra, and produce a reliable estimate of the goodness of fit of the given model. We apply this technique to constrain the broad-band power spectra of a sample of four Seyfert galaxies monitored by the Rossi X-ray Timing Explorer (RXTE) over three years. We show that the power spectra of three of the AGN in our sample (MCG-6-30-15, NGC 5506 and NGC 3516) flatten significantly towards low frequencies, while the power spectrum of NGC 5548 shows no evidence of flattening. We fit two models for the flattening: a ‘knee’ model, analogous to the low-frequency break seen in the power spectra of BHXRBs in the low state (where the power-spectral slope flattens to α=0), and a ‘high-frequency break’ model (where the power-spectral slope flattens to α=1), analogous to the high-frequency break seen in the high- and low-state power spectra of the classic BHXRB Cyg X-1. Both models provide good fits to the power spectra of all four AGN. For both models, the characteristic frequency for flattening is significantly higher in MCG-6-30-15 than in NGC 3516 (by a factor of ∼10), although both sources have similar X-ray luminosities, suggesting that MCG-6-30-15 has a lower black hole mass and is accreting at a higher rate than NGC 3516. Assuming linear scaling of characteristic frequencies with black hole mass, the high accretion rate implied for MCG-6-30-15 favours the high-frequency break model for this source, and further suggests that MCG-6-30-15, and possibly NGC 5506, may be analogues of Cyg X-1 in the high state. Comparison of our model fits with naive fits, where the model is fitted directly to the observed power spectra (with errors estimated from the data), shows that Monte Carlo fitting is essential for reliably constraining the broad-band power spectra of AGN light curves obtained to date.