We compute black hole masses and bolometric luminosities for 87 obscured active galactic nuclei (AGNs) in the redshift range 0.25 ≤ z ≤ 1.25, selected from the GOODS deep multi-wavelength survey fields via their X-ray emission. We fit the optical images and obtain morphological parameters for the host galaxy, separating the galaxy from its central point source, thereby obtaining a four-band optical spectral energy distribution (SED) for each active nucleus. We calculate bolometric luminosities for these AGNs by reddening a normalized mean SED of GOODS broad-line AGNs to match the observed central point-source SED of each obscured AGN. This estimate of L bol has a smaller spread than simple bolometric corrections to the X-ray luminosity or direct integration of the observed multi-wavelength SED, suggesting it is a better measure. We estimate central black hole masses from the bulge luminosities. The black hole masses span a wide range, 7 × 106 M ☉ to 6 × 109 M ☉; the median black hole mass is 5 × 108 M ☉. The majority of these AGNs have L/L Edd ≤ 0.01, and we detect no significant evolution of the mean Eddington ratio to z = 1.25. This implies that the bulk of black hole growth in these obscured AGNs must have occurred at z gsim 1 and that we are observing these AGNs in a slow- or no-growth state.