Facing the SARS-CoV-2 epidemic requires intensive testing on the population to early identify and isolate infected subjects. During the first emergency phase of the epidemic, RT-qPCR on nasopharyngeal (NP) swabs, which is the most reliable technique to detect ongoing infections, exhibited limitations due to availability of reagents and budget constraints. This stressed the need to develop screening procedures that require fewer resources and are suitable to be extended to larger portions of the population. RT-qPCR on pooled samples from individual NP swabs seems to be a promising technique to improve surveillance. We performed preliminary experimental analyses aimed to investigate the performance of pool testing on samples with low viral load and we evaluated through Monte Carlo (MC) simulations alternative screening protocols based on sample pooling, tailored to contexts characterized by different infection prevalence. We focused on the role of pool size and the opportunity to develop strategies that take advantage of natural clustering structures in the population, e.g. families, school classes, hospital rooms. Despite the use of a limited number of specimens, our results suggest that, while high viral load samples seem to be detectable even in a pool with 29 negative samples, positive specimens with low viral load may be masked by the negative samples, unless smaller pools are used. The results of MC simulations confirm that pool testing is useful in contexts where the infection prevalence is low. The gain of pool testing in saving resources can be very high, and can be optimized by selecting appropriate group sizes. Exploiting natural groups makes the definition of larger pools convenient and potentially overcomes the issue of low viral load samples by increasing the probability of identifying more than one positive in the same pool.