Having a reliable understanding of bank telemarketing performance is of great importance in the modern world of economy. Recently, machine learning models have obtained high attention for this purpose. In order to introduce and evaluate cutting-edge models, this study develops sophisticated hybrid models for estimating the success rate of bank telemarketing. A large free dataset is used which lists the clients’ information of a Portuguese bank. The data are analyzed by four artificial neural networks (ANNs) trained by metaheuristic algorithms, namely electromagnetic field optimization (EFO), future search algorithm (FSA), harmony search algorithm (HSA), and social ski-driver (SSD). The models predict the subscription of clients for a long-term deposit by evaluating nineteen conditioning parameters. The results first indicated the high potential of all four models in analyzing and predicting the subscription pattern, thereby, revealing the competency of neuro-metaheuristic hybrids. However, comparatively speaking, the EFO yielded the most reliable approximation with an area under the curve (AUC) around 0.80. FSA-ANN emerged as the second-accurate model followed by the SSD and HSA with respective AUCs of 0.7714, 0.7663, and 0.7160. Moreover, the superiority of the EFO-ANN is confirmed against several conventional models from the previous literature, and finally, it is introduced as an effective model to be practically used by banking institutions for predicting the likelihood of deposit subscriptions.