Biological cells naturally exchange information for adapting to the environment, or even influencing other cells. One of the latest frontiers of synthetic biology stands in engineering cells to harness these natural communication processes for tissue engineering and cancer treatment, amongst others. Although experimental success has been achieved in this direction, approaches to characterize these systems in terms of communication performance and their dependence on design parameters are currently limited. In contrast to more classical communication systems, information in biological cells is propagated through molecules and biochemical reactions, which in general result in nonlinear input-output behaviors with system-evolution-dependent stochastic effects that are not amenable to analytical closed-form characterization. In this paper, a computational approach is proposed to characterize the information exchange in these systems, based on stochastic simulation of biochemical reactions and the estimation of information-theoretic parameters from sample distributions. In particular, this approach focuses on engineered cell-to-cell communications with a single transmitter and receiver, and it is applied to characterize the performance of a realistic system. Numerical results confirm the feasibility of this approach to be at the basis of future forward engineering practices for these communication systems.