Conformal Prediction (CP) is a method that can be used for complementing the bare predictions produced by any traditional machine learning algorithm with measures of confidence. CP gives good accuracy and confidence values, but unfortunately it is quite computationally inefficient. This computational inefficiency problem becomes huge when CP is coupled with a method that requires long training times, such as Neural Networks. In this paper we use a modifi- cation of the original CP method, called Inductive Confor- mal Prediction (ICP), which allows us to construct a Neural Network confidence predictor without the massive computa- tional overhead of CP. The method we propose accompanies its predictions with confidence measures that are useful in practice, while still preserving the computational efficiency of its underlying Neural Network.