In a method and magnetic resonance apparatus to determine a B0 field map describing the local deviation from a nominal Larmor frequency of the magnetic resonance apparatus, magnetic resonance data are acquired at at least two different dephasing times after an excitation, in measurements implemented at two different echo times whose difference forms a dephasing time, and a phase change used to determine the B0 field map is determined from a difference of phases measured at different echo times. The phase changes of different dephasing times are evaluated to at least partially reduce an ambiguity due to Nyquist phase wrapping. The measurements for different dephasing times are implemented at least in part with excitations that generate different excitation fields.