The aim of this study is to develop a modeling procedure based on using artificial neural networks (ANNs) for predicting the frequency-dependent behavior of a microwave split-ring resonator (SRR) used for the dielectric characterization of liquid samples. The SRR device was designed and fabricated using the inkjet printing technology and, then, calibrated by means of water/ethanol mixtures with varying concentrations. By observing the variations in the forward transmission coefficient (i.e., $S_{21})$ of the studied microwave device, a frequency shift of the resonant frequency and variations in the magnitude of $S_{21}$ were recorded, which were related to the ethanol volume fraction. Using this calibration data, an ANN-based model is developed, which takes the ethanol volume fraction as input feature and, then, predicts the SRR sensor resonant parameters. The accuracy of the ANN-based model is reported and discussed.