Stochastic mapping is frequently used in comparative biology to simulate character evolution, enabling the probabilistic computation of statistics such as number of state transitions along a tree and distribution of states in its internal nodes. Common implementations rely on Continuous-time Markov Chain simulations whose parameters are difficult to adjust and subjected to inherent inaccuracy. Thus, researchers must run a large number of simulations in order to obtain adequate estimates. Although execution time tends to be relatively small when simulations are performed on a single tree assumed to be the true topology, it may become an issue if analyses are conducted on several trees, such as the ones that make up posterior distributions obtained via Bayesian phylogenetic inference. Working with such distributions is preferable to working with a single tree, for they allow the integration of phylogenetic uncertainty into parameter estimation. In such cases, detailed character mapping becomes less important than parameter integration across topologies. Here, we present an R-based implementation (SFREEMAP) of an analytical approach to obtain accurate, per-branch expectations of numbers of state transitions and dwelling times. We also introduce an intuitive way of visualizing the results by integrating over the posterior distribution and summarizing the parameters onto a target reference topology (such as a consensus or MAP tree) provided by the user.