The design of a multichannel system of stabilization of the magnetic resonance of ultracold neutrons in a multichamber spectrometer developed in the search for the electric dipole moment (EDM) of the neutron is briefly described. The results of tests on a prototype of this system are presented, which show the possibility of ensuring the stability of resonance lines that is equivalent to a magnetic field variation not exceeding ∼30 fT over a 100-s period of EDM measurements.