The process of electron flow spin-polarization in a waveguide with two narrows in magnetic field is investigated. Asymptotic formulas for the main characteristics of resonant tunneling for 'sufficiently small' diameters of the waveguide's narrows are presented. They contain constants, which are found numerically by solving some auxiliary problems. Also, we obtain the same characteristics of the process by means of numerical calculation of the waveguide's scattering matrix. The obtained results show that asymptotic and numerical methods give equivalent outcomes at wide band of the narrows' diameters. The numerical method becomes ill-conditioned as the diameter decreases. However, the asymptotics remains reliable at such condition. On the other hand, the asymptotics gives way to the numerical method as the diameter increases; in fact, for wide narrows the resonant tunneling vanishes by itself.