We propose a Nambu Jona-Lasinio (NJL) effective model of relativistic superconductivity. In this framework, we discuss possible electromagnetic (EM) behaviors of (specifically) type-II superconductivity in line with the nonrelativistic Ginzburg-Landau (GL) theory. We comment on possible solitonic solutions of this model. Our investigation could be of relevance to describe type-II proton superconductivity in neutron-star crusts.