Artificial neural networks and heuristic algorithms are popular intelligent techniques in solving complex engineering problems. This article presents new approaches based on feed-forward artificial neural networks trained with Levenberg-Marquardt, touring ant colony optimization, and parallel ant colony optimization algorithms to determine the resonant frequencies of the rectangular, circular, and triangular microstrip antennas. The results achieved from heuristic- and gradient-based algorithms were compared to that of the other methods in the literature. The results obtained from the neural models for the various microstrip antennas are in very good agreement with the experimental results in the literature. The proposed neural model trained with parallel ant colony optimization algorithm provides better accuracy than the other algorithms presented in this article and the literature.