The process of designing microwave devices is difficult and time-consuming because the analytical and numerical methods used in the design process are complex. Therefore, it is necessary to search for new methods that will allow for an acceleration of synthesis and analytic procedures. This is especially important in cases where the procedures of synthesis and analysis have to be repeated many times, until the correct device configuration is found. Artificial neural networks are one of the possible alternatives for the acceleration of the design process. In this paper we present a procedure for analyzing a hybrid meander system (HMS) using the feed-forward backpropagation network (FFBN). We compared the prediction results of the transmission factor and the reflection factor , obtained using the FFBN, with results obtained using traditional analytical and numerical methods, as well as with experimental results. The comparisons show that prediction results significantly depend on the FFBN structure. In terms of the lowest difference between the characteristics calculated using the method of moments (MoM) and characteristics predicted using the FFBN, the best prediction was achieved using the FFBN with three hidden layers, which included 18 neurons in the first hidden layer, 14 neurons in the second hidden layer, and 2 neurons in the third hidden layer. Differences between the predicted and calculated results did not exceed 7% for the parameter and 5% for the parameter. The prediction of parameters using the FFBN allowed the analysis procedure to be sped up from hours to minutes. The experimental results correlated with the predicted characteristics.