In the literature, it is argued that Deep Neural Networks (DNNs) possess a certain degree of robustness mainly for two reasons: their distributed and parallel architecture, and their redundancy introduced due to over provisioning. Indeed, they are made, as a matter of fact, of more neurons with respect to the minimal number required to perform the computations. It means that they could withstand errors in a bounded number of neurons and continue to function properly. However, it is also known that different neurons in DNNs have divergent fault tolerance capabilities. Neurons that contribute the least to the final prediction accuracy are less sensitive to errors. Conversely, the neurons that contribute most are considered critical because errors within them could seriously compromise the correct functionality of the DNN. This paper presents a software methodology based on a Triple Modular Redundancy technique, which aims at improving the overall reliability of the DNN, by selectively protecting a reduced set of critical neurons. Our findings indicate that the robustness of the DNNs can be enhanced, clearly, at the cost of a larger memory footprint and a small increase in the total execution time. The trade-offs as well as the improvements are discussed in the work by exploiting two DNN architectures: ResNet and DenseNet trained and tested on CIFAR-10.