An artificial neural network (ANN) is proposed to predict the input impedance of a broadband antenna as a function of its geometric parameters. The input resistance of the antenna is first parameterized by a Gaussian model, and the ANN is constructed to approximate the nonlinear relationship between the antenna geometry and the model parameters. Introducing the model simplifies the ANN and decreases the training time. The reactance of the antenna is then constructed by the Hilbert transform from the resistance found by the neuromodel. A hybrid gradient descent and particle swarm optimization method is used to train the neural network. As an example, an ANN is constructed for a loop antenna with three tuning arms. The antenna structure is then optimized for broadband operation via a genetic algorithm that uses input impedance estimates provided by the trained ANN in place of brute-force electromagnetic computations. It is found that the required number of electromagnetic computations in training the ANN is ten times lower than that needed during the antenna optimization process, resulting in significant time savings