Modern fiber-optic communication networks must be vetted against a strict standard of robustness: they cannot allow more than 1 lost bit for every 109 bits transmitted. While numerical simulations are a valuable tool in establishing bit error ratios of complicated systems, it is often impossibly expensive to run sufficiently many sample simulations to resolve events that have such low probability of occurring in a "hit-or-miss" Monte Carlo approach. I will present a hybrid method that combines a common variance-reduction method known as importance sampling and different finite-dimensional reduction techniques (e.g., soliton perturbation theory, variational methods) to resolve low-probability events with greatly improved (often by several orders of magnitude) efficiency. The last portion of my talk will be devoted to generalizing this approach by framing it in the context of renormalization group theory.