We demonstrate that superconductors with broken inversion symmetry support a family of stable, spatially localized configurations of the self-knotted magnetic field. These solutions, which we term “toroflux,” are the superconducting counterparts of the Chandrasekhar-Kendall states (spheromaks) that appear in highly conducting, force-free astrophysical and nuclear-fusion plasmas. The superconducting torofluxes are solutions of superconducting models, in the presence of a parity-breaking Lifshitz invariant associated with the Formula Presented point-group symmetry. These solutions are characterized by a nonvanishing helicity of the magnetic field, and also by a toroidal dipole moment of the magnetic field. We demonstrate that a magnetic dipole or a ferromagnetic inclusion in the bulk of a noncentrosymmetric superconductor sources finite-energy toroflux solutions.