Results of electron spin resonance studies of copper pyrimidine dinitrate (Cu-PM, [PM-Cu(NO3)(2)(H2O)(2)] (n) , PM = pyrimidine), a spin-1/2 antiferromagnetic chain material with alternating g-tensor and Dzyaloshinskii-Moriya interactions, in pulsed magnetic fields up to 63 T are reported. The field-induced gap shows a non-monotonic behavior with a minimum in the vicinity of the saturation field H (sat) =48.5 T. This is associated with a transition from the sine-Gordon region to a spin-polarized state with magnon excitations. By comparing the entire set of experimental data with results of density matrix renormalization group calculations for Cu-PM, the validity of the used theoretical approach is proven.