Magnetic chemically peculiar stars of the main sequence can present rotational periods as long as many decades. Here we report the results of an observational campaign started in 2001 aimed at establishing these very long periods from the variability of the integrated magnetic field modulus, the so-called surface magnetic field Bs, as measured from the Zeeman splitting of the Fe II 6149.258 Å spectral line. 36 stars have been monitored with various high-resolution spectrographs at different telescopes, totalling 412 newly collected spectra. To improve the phase coverage, we have also exploited all public archives containing high-resolution spectra, many not yet published. On the basis of these new Bs variability curves, we (1) confirm or revisit the periods of 24 stars, (2) extend the lower limits to the periods of HD 55719 (P > 38 yr), HD 165474 (P > 27 yr), and HD 177765 (P > 37 yr), (3) establish for the first time the periods of HD 29578 (P = 10.95 yr), HD 47103 (P = 17.683 d), HD 150562 (P = 5.7 yr), and HD 216018 (P = 34.044 d), and (4) set lower limits to the periods of HD 75445 (P »14 yr), HD 110066 (P » 29 yr), HD 116114 (P > 48 yr), and HD 137949 (P > 27 yr). As to γ Equ, whose period must exceed 90 yr, we point out a clear decrease in the field modulus, the maximum of which coincides within the uncertainties with the minimum of the variation in the integrated longitudinal field.