An inverse method for parameters estimation of infinite cylinders (the dielectric properties, location, and radius) in two dimensions from amplitude-only microwave information is presented. To this end two different Artificial Neural Networks (ANN) topologies are compared; Multilayer Perceptron (MLP) and a Convolutional Neural Network (CNN). Several simulations employing the Finite Differences in Time Domain (FDTD) method are performed to solve the direct electromagnetic problem and generate training, validation, and test sets for the ANN models. The magnitude of the mean errors in estimating the position and size of the cylinder are up to (1.9 $\pm$ 3.3) mm and (0.2 $\pm$ 0.8) mm for the MLP and CNN, respectively. The magnitude of the mean percentage relative errors in estimating the dielectric properties of the cylinder are up to (6.5 $\pm$ 13.8) % and (0.0 $\pm$ 7.2) % for the MLP and CNN, respectively. The errors in the parameters estimation from the MLP model are low, however, significantly lower errors were obtained with the CNN model. A validation example is shown using a simulation in three dimensions. Measurement examples with homogeneous and heterogeneous cylinders are presented aiming to prove the feasibility of the described method.