We discuss the phenomenology of damping signatures in the neutrino oscillation probabilities, where either the oscillating terms or the probabilities can be damped. This approach is a possibility for tests of damping effects in future neutrino oscillation experiments, where we mainly focus on reactor and long-baseline experiments. We extensively motivate different damping signatures due to small corrections by neutrino decoherence, neutrino decay, oscillations into sterile neutrinos, or other mechanisms, and classify these signatures according to their energy (spectral) dependencies. We demonstrate, at the example of short baseline reactor experiments, that damping can severely alter the interpretation of results, e.g., it could fake a value of sin²θ₁₃ smaller than the one provided by Nature. In addition, we demonstrate how a neutrino factory could constrain different damping models with emphasis on how these different models could be distinguished, i.e., how easily the actual type of effect could be identified. We find that the damping models cluster in different categories, which can be much better distinguished from each other than models within the same cluster.