The computation of statistical properties of RNA structure at the thermodynamic equilibrium, or Boltzmann ensemble of low free-energy, represents an essential step to understand and harness the selective pressure weighing on RNA evolution. However, classic methods for sampling representative conformations are frequently crippled by large levels of redundancy, which are uninformative and detrimental to downstream analyses. In this work, we adapt and implement, within the Vienna RNA package, an efficient non-redundant backtracking procedure to produce collections of unique secondary structures generated within a well-defined distribution. This procedure is coupled with a novel statistical estimator, which we prove is unbiased, consistent and has lower variance (better convergence) than the classic estimator. We demonstrate the efficiency of our coupled non-redundant sampler/estimator by revisiting several applications of sampling in RNA bioinformatics, and demonstrate its practical superiority over previous estimators. We conclude by discussing the choice of the number of samples required to produce reliable estimates.