When an artificial neural network is used to determine the value of a physical quantity its result is usually presented without an uncertainty. This is due to the difficulty in determining the uncertainties related to the neural model. However, the result of a measurement can be considered valid only with its respective measurement uncertainty. Therefore, this article proposes a method of obtaining reliable results by measuring systems that use artificial neural networks. For this, it considers the Monte Carlo Method (MCM) for propagation of uncertainty distributions during the training and use of the artificial neural networks.