The eikonal quasinormal modes (QNMs) of rotating regular black holes (RBHs) are shown to have a correspondence with the BH shadow radius. This correspondence is established by linking the real part of eikonal QNMs to the shadow radius, which is determined by the properties of null geodesics. The key requirement for this correspondence to hold is that the Hamilton-Jacobi equation for null geodesics and the Klein-Gordon equation must be separable. Metrics obtained via the Newman-Janis algorithm, under certain mathematical conditions, satisfy these separability requirements. The rotating Bardeen and Hayward RBHs, which are regular in the sense of having finite curvature invariants, are shown to satisfy these conditions. The eikonal QNM-shadow radius correspondence is verified for these metrics, demonstrating that the correspondence holds for a wide range of axisymmetric space-times beyond Kerr. This opens the possibility for strong-field multi-messenger tests of fundamental physics by combining gravitational wave spectroscopy and VLBI imaging of BHs. The results show excellent agreement between the shadow radius calculated from eikonal QNMs and those derived from closed photon orbits, confirming the validity of the correspondence for rotating regular BHs.The eikonal quasinormal modes (QNMs) of rotating regular black holes (RBHs) are shown to have a correspondence with the BH shadow radius. This correspondence is established by linking the real part of eikonal QNMs to the shadow radius, which is determined by the properties of null geodesics. The key requirement for this correspondence to hold is that the Hamilton-Jacobi equation for null geodesics and the Klein-Gordon equation must be separable. Metrics obtained via the Newman-Janis algorithm, under certain mathematical conditions, satisfy these separability requirements. The rotating Bardeen and Hayward RBHs, which are regular in the sense of having finite curvature invariants, are shown to satisfy these conditions. The eikonal QNM-shadow radius correspondence is verified for these metrics, demonstrating that the correspondence holds for a wide range of axisymmetric space-times beyond Kerr. This opens the possibility for strong-field multi-messenger tests of fundamental physics by combining gravitational wave spectroscopy and VLBI imaging of BHs. The results show excellent agreement between the shadow radius calculated from eikonal QNMs and those derived from closed photon orbits, confirming the validity of the correspondence for rotating regular BHs.