Both future 100 km in circumference electron-positron colliders CEPC and FCC-ee want know beams energies with the extreme precision of 1-2 ppm. This can be done only with the help of the well-known resonant depolarization technique. Still, some beam parameters of these machines, like energy spread and radiative damping decrements, becomes so high near or above 80 GeV per beam, that it is required special consideration and tricks to overcome all the difficulties. The author has written a simple spin tracking code, which simulates main features of the resonant depolarization process in presence of continuous energy diffusion due to synchrotron radiation fluctuations. By running this code with different beam parameters it was shown that resonant depolarization technique works at 80 GeV only if the synchrotron oscillation frequency tune is chosen above 0.075. The alternative to the resonant depolarization technique approach, based on detection of free precession of spins flipped into the horizontal plane, was proposed by the author and the related results are analyzed. As it was shown, the applicability of this method is limited only by the attainable statistical accuracy of the turn by turn measurement of the longitudinal polarization component. Future longitudinal laser polarimeters shall provide the needed for such measurements sensitivity in the order of 0.01-0.02 per one turn.