A brief description of the phenomenology of an extra neutral gauge boson (Z') and of its search in CMS will introduce the original part of this thesis work, which is concerned with the calibration of the magnetic field in the CMS barrel using cosmic muons. In the analysis of a heavy $Z'$ decaying into muons pairs, it will be of key importance to have a good knowledge of the dimuon mass resolution. An imperfect modellization of the magnetic field could impair the mass measurement. The magnetic field inside the CMS return yokes will be known from the interpolation to a grid of values computed by a finite-elements program. A way to calibrate the field map in the yokes w.r.t. the central, solenoidal field is to exploit the redundancy offered by the muons system: pointing cosmic muons can be tracked both with the inner silicon tracker, immersed in the solenoidal field, and with the muons chambers, hosted inside the yokes. Two original track-based calibration algorithms are described and, then, applied to a sample of cosmic muons collected by CMS.