  We use the Relativistic Precession Model (RPM) (Stella et al. 1999a) 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 extend the techniques outlined by Motta et al. (2014a,b) to use pairs of
simultaneously measured QPOs, rather than triplets, and extend the underlying
spacetime 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 spacetime 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 we
constrain particular deviations from GR to be less than one part per thousand.
