Sandwich plates are commonly subjected to transverse shear force during their service and exhibit vibration phenomena. The presence of geometrical discontinuities or fabrication defects like cracks, pores, and holes in the sandwich structure can significantly reduce its stiffness and influence the natural frequency of the plate. This paper proposed a metamodeling approach based on the higher-order extended finite element method (HOXFEM) and artificial neural network (ANN) to predict natural frequency response of a cracked sandwich plate. A higher-order shear deformation theory (HSDT) is employed for laminated sandwich plates. In the presented HOXFEM method, crack tip enrichment functions are revised for better computational accuracy and computational time. Only four crack tip enrichment functions are proposed in HOXFEM, instead of the eight enrichment functions used in classical XFEM approach. These four enrichment functions consist of two enrichment functions for displacement degrees of freedom and two enrichment functions for rotational degrees of freedom. Further, optimized neural network architecture (4-10-10-10-1) is constructed with data obtained from HOXFEM simulation. The efficacy of the proposed methodology is established through the application of various numerical examples. These examples include different crack sizes and various small cracks/holes configurations within the sandwich plate under different boundary conditions.