Measuring information transmission from stimulus to response is useful for evaluating the signaling fidelity of biochemical reaction networks (BRNs) in cells. Quantification of information transmission can reveal the optimal input stimuli environment for a BRN and the rate at which the signaling fidelity decreases for non-optimal input probability distributions. Here we present sparse estimation of mutual information landscapes (SEMIL), a method to quantify information transmission through cellular BRNs using commonly available data for single-cell gene expression output, across a design space of possible input distributions. We validate SEMIL and use it to analyze several engineered cellular sensing systems to demonstrate the impact of reaction pathways and rate constants on mutual information landscapes.