In many engineering contexts it is easy to state what we want but hard to achieve our desired outcomes. The more potential solutions exist, the harder it becomes to identify optimal solutions. Here we show how this problem can be approached in an approximate Bayesian computation framework. Our approach has the advantage that it builds on the powerful Bayesian model selection formalism, includes sensitivity and robustness analysis at no extra cost, and flexibly incorporates diverse design objectives. We illustrate the performance of this approach in the context of bacterial two-component systems (TCS). These systems enable prokaryotes (and some simple eukaryotes and plants) to sense their environments and adapt their internal state to changing circumstances. We present a detailed analysis of orthodox and unorthodox TCSs and show how we can rationally construct TCS that show robust and optimal response characteristics to different stimuli encountered during bacterial infections or in biotechnological (e.g. biofuels production and bioremediation) applications. We conclude by elaborating on the connections between our approach and maximum-entropy procedures and the advantages over traditional engineering strategies.