This paper shows that Ridge Polynomial Neural Networks (RPNN) and Least-Square Support Vector Machines (LS-SVM) technique provide efficient tools for microwave characterization of dielectric materials. Such methods avoids the slow learning properties of multilayer perceptrons (MLP) which utilize computationally intensive training algorithms and can get trapped in local minima. RPNN and LS-SVM are combined in this work with the Finite Element Method (FEM) to evaluate the dielectric materials properties. The RPNN is constructed from a number of increasing orders of Pi-Sigma units, it maintains fast learning properties and powerful mapping capabilities of single layer High Order Neural Networks (HONN). LS-SVM is a statistical learning method that has good generalization capability and learning performance. The FEM is used to create the data set required to train the RPNN and LS-SVM. The performance of a LS-SVM model depends on a careful setting of its associated hyper-parameters. In this study the LS-SVM hyper-parameters are optimized by using a Bayesian regularization technique. Results show that LS-SVM can achieve good accuracy and faster speed than neural network methods.