The mono- and bidomain models lead to travelling waves with sharp gradients neighboring regions with small variations of the solution. Anisotropic mesh adaptation allows a substantial reduction of the number of degrees of freedom while providing very accurate solutions. Such approaches have been applied to the mono- and bidomain models using heuristic a priori metric-based estimators. We propose an a posteriori error estimator that accounts for the error in time and space for all variables, including the trans-membrane and gating variables. Numerical results will be shown. This is a joint work with my former PhD student, Edward Boey, and a colleague, Thierry Giordano.