The masses of 68 supermassive black holes (SMBHs) in nearby (z<0.15) active galactic nuclei (AGNs) detected by the INTEGRAL observatory in the hard X-ray energy band (17-60 keV) outside the Galactic plane (|b| > 5 degrees) have been estimated. Well-known relations between the SMBH mass and (1) the infrared luminosity of the stellar bulge (from 2MASS data) and (2) the characteristics of broad emission lines (from RTT-150 data) have been used. A comparison with the more accurate SMBH mass estimates obtained by the reverberation-mapping technique and from direct dynamical measurements is also made for several objects. The SMBH masses derived from the correlation with the bulge luminosity turn out to be systematically higher than the estimates made by other methods. The ratio of the bolometric luminosity to the critical Eddington luminosity has been found for all AGNs. It ranges from 1 to 100% for the overwhelming majority of objects.