The increase of distributed energy resources in the smart grid calls for new ways to profitably exploit these resources, which can participate in day-ahead ancillary energy markets by providing flexibility. Higher profits are available for resource owners that are able to anticipate price peaks and hours of low prices or zero prices, as well as to control the resource in such a way that exploits the price fluctuations. Thus, this study presents a solution in which artificial neural networks are exploited to predict the day-ahead ancillary energy market prices. The study employs the frequency containment reserve for the normal operations market as a case study and presents the methodology utilized for the prediction of the case study ancillary market prices. The relevant data sources for predicting the market prices are identified, then the frequency containment reserve market prices are analyzed and compared with the spot market prices. In addition, the methodology describes the choices behind the definition of the model validation method and the performance evaluation coefficient utilized in the study. Moreover, the empirical processes for designing an artificial neural network model are presented. The performance of the artificial neural network model is evaluated in detail by means of several experiments, showing robustness and adaptiveness to the fast-changing price behaviors. Finally, the developed artificial neural network model is shown to have better performance than two state of the art models, support vector regression and ARIMA, respectively