Purpose <p>This research proposes novel computational methods, namely the Ritz–Hermite and Ritz–Laguerre methods, for the analysis of porous metal foam (PMF) microplates.</p> Method <p>The analysis is based on higher-order shear deformation theory and modified couple stress theory, incorporating a constant material length scale parameter. The dynamic responses of the microplates under an explosive blast load are determined using Newmark’s technique. The proposed Ritz method employs orthogonal polynomial-generated shape functions, constructed as hybrid functions by combining a base polynomial with a series of orthogonal polynomials (Hermite and Laguerre), ensuring compliance with required boundary conditions.</p> Results and Conclusion <p>The proposed methods exhibit superior convergence speed and stability compared to alternative shape functions. The study presents, for the first time, the dynamic responses of PMF microplates under various loads, including explosive blasts, triangular, and rectangular patterns. The research investigates the effects of the material length scale parameter, damping factor, side-to-thickness ratio, porosity coefficient, porosity distribution, and boundary conditions on the vibration, buckling, and transient responses of PMF microplates. The findings, supported by numerical results, highlight the efficiency and accuracy of the proposed computational methods in predicting the structural characteristics of PMF microplates.</p>