By numerically solving models with competing superconducting and antiferromagnetic orders, we study the magnetic field dependence of the antiferromagnetic moment in both the weak and strong field regimes. Through a comparison with the neutron scattering results of Kang et al. and Matsuura et al. on Nd(1.85)Ce(0.15)CuO4, we conclude that this system is close to a SO(5) symmetric critical point. We also make a quantitative prediction on increasing the upper critical field B(c2) and the superconducting transition temperature T(c) by applying an in-plane magnetic field.