ABSTRACT We use the Relativistic Precession Model (RPM) and quasi-periodic oscillation (QPO) observations from the Rossi X-ray Timing Explorer to derive constraints on the properties of the black holes that power these sources and to test general relativity (GR) in the strong field regime. We build upon past techniques by using pairs of simultaneously measured QPOs, rather than triplets, and by including characteristic frequencies from the broad noise components of the power spectra in our fits. We find the inclusion of these broad noise components causes an overestimate in masses and underestimate in spins compared to values derived independently from optical spectra. We extend the underlying space-time metric to constrain potential deviations from the predictions of GR for astrophysical black holes. To do this, we modify the RPM model to a Kerr–Newman–deSitter space-time and model changes in the radial, ecliptic, and vertical frequencies. We compare our models with X-ray data of XTE J1550-564 and GRO J1655-40 using robust statistical techniques to constrain the parameters of the black holes and the deviations from GR. For both sources, using QPO and characteristic frequency data, we constrain particular deviations from GR to be less than one part per thousand.