A technique based on artificial neural network (ANN) is proposed to extract electromagnetic properties of reflection-asymmetric samples from reference-plane-invariant scattering parameter measurements. It first determines reference plane transformation distances and then extract material properties. The number of neurons in the hidden layer of the ANN model was evaluated subject to accuracy and time constraints. We examined the conformity of the dataset of the ANN model and the required time for the training process by considering different number of neurons in the selected hidden layer. S-parameter waveguide measurements at X-band (8.2-12.4 GHz) of two bianisotropic metamaterial slabs, as reflection-asymmetric samples, composed of square-shaped split-ring-resonators and asymmetrically positioned into their measurement cells were used to validate the ANN model and evaluate the effectiveness of the proposed method in extracting the electromagnetic properties.