In this talk we explore robustness of a-posteriori estimators for finite-element solutions of elliptic boundary value problems with respect to coefficients of the problem. First we present an overview of estimators for a scalar reaction-diffusion equation and discuss robustness of a particular class of estimators for a singularly perturbed reaction-diffusion problem developed by R.Verfuerth. Next we give an introduction to modeling physical problems in which reaction-diffusion problems arise and in particular we explain principles of modeling chemically reacting systems using differential equations. These applications motivate our study of a coupled system of reaction-diffusion equations which can be cast in a general abstract form of a system coupled by a monotone operator. Last we propose an a-posteriori estimator of residual type for the steady-state version of the system. The talk will be illustrated by numerical results.