We present a brief overview of the main properties of electromagnetic fields of regular rotating electrically charged objects in non-linear electrodynamics minimally coupled to gravity (NED-GR). The basic features of electromagnetic fields follow from the analysis of the regular solutions to the NED-GR dynamic equations. For NED-GR regular objects the Lagrangian inevitably branches at a single minimum of the field invariant F. The study of the asymptotic of the solutions of the field equations at r → 0 reveals the fundamental features of the electromagnetic dynamics on the de Sitter vacuum disk (r = 0) in the deep interiors of rotating NED-GR objects. The disk has the properties of a perfect conductor and an ideal diamagnetic, zero magnetic induction, and is confined by a ring with a superconducting current, which replaces the Kerr ring singularity, serves as a non-dissipative source of electromagnetic fields of NED-GR regular objects and provides the origin of their intrinsic magnetic momenta.