Encouraging exploration, typically by preserving the diversity within the population, is one of the most common method to improve the behavior of evolutionary algorithms with deceptive fitness functions. Most of the published approaches to stimulate exploration rely on a distance between genotypes or phenotypes; however, such distances are difficult to compute when evolving neural networks due to (1) the algorithmic complexity of graph similarity measures, (2) the competing conventions problem and (3) the complexity of most neural-network encodings. In this paper, we introduce and compare two conceptually simple, yet efficient methods to improve exploration and avoid premature convergence when evolving both the topology and the parameters of neural networks. The two proposed methods, respectively called behavioral novelty and behavioral diversity are built on multiobjective evolutionary algorithms and on a user-defined distance between behaviors. They can be employed with any genotype. We benchmarked them on the evolution of a neural network to compute a Boolean function with a deceptive fitness. The results obtained with the two proposed methods are statistically similar to those of NEAT and substantially better than those of the control experiment and of a phenotype-based diversity mechanism.