  Precisely determining the gap voltage and phase in an RF cavity is essential
for the calibration of the LLRF feedbacks. Following the conventional approach,
measured RF power is converted into gap voltage, assuming a given shunt
impedance. However, power and impedance evaluations can both have large
uncertainties. Alternatively, the voltage can be obtained precisely with a
technique based on longitudinal phase-space tomography. From a set of bunch
profiles, tomography reconstructs the bunch distribution in the longitudinal
phase-space. The quality of the reconstruction strongly depends on the RF
voltage and therefore allows to derive its absolute value. In this paper we
describe the tomography-based voltage measurements performed in the CERN PSB
and SPS, where this method allowed to detect significant voltage errors for the
main RF systems. After applying the correction factors in the LLRF, 1\%
accuracies were reached. We report here also the remarkable results achieved by
using this technique to calibrate the voltage of the SPS higher-harmonic
cavities at 800 MHz, as well as their relative phases with respect to the 200
MHz cavities.
