Here is an extract of a lecture I gave in the 2014 Frascati Spring school, which explains the principle of energy calibration with resonant depolarization at LEP in some details (as well as the effect of the moon on the measurement).
At LEP, the energy calibration was performed after the collision periods, and the measurement had to be extrapolated back to the runnning conditions, with the corresponding systematic uncertainty of 2 MeV on the beam energy. At the FCC-ee, the number of bunches is large enough (more than 10,000 at the Z pole!) to select of few pilot bunches - say 100 bunches - which would not collide, and on which resonant depolarization could be applied while the other bunches are colliding. The systematic uncertainty related to the extrapolation would therefore disappear, and each of the 100 measurements would have a precision better than 0.1 MeV on the beam energy.