Recently metamaterials made of periodic nanowire arrays, multilayers, and grating structures have been studied for near-field thermal radiation with enhanced coupling of evanescent waves due to surface plasmon/phonon polariton, hyperbolic mode, epsilon-near-zero and epsilon-near-pole (ENP) modes, guided mode, and wave interference. In this work, both effective uniaxial electric permittivity and magnetic permeability of a nanowire-based metamaterial are retrieved theoretically through the far-field radiative properties obtained by finite difference time-domain (FDTD) simulations. The artificial magnetic response of metamaterials, which cannot be obtained by traditional effective medium theory (EMT) based on electric permittivity of constitutes only, is successfully captured by the nonunity magnetic permeability, whose resonant frequency is verified by an inductor-capacitor model. By incorporating the retrieved electric permittivity and magnetic permeability into fluctuational electrodynamics with multilayer uniaxial wave optics, the near-field radiative heat transfer between the metallic nanowire arrays is theoretically studied and spectral near-field heat enhancements are found for both transverse electric and magnetic waves due to artificial magnetic resonances. The understanding and insights obtained here will facilitate the application of metamaterials in near-field radiative transfer.