A coarse-grained kinetic Monte Carlo (CG-KMC) method was recently introduced as a hierarchical multiscale modeling tool for extending the length scales reached by stochastic simulations. Coarse-graining causes errors due to loss of degrees of freedom. To quantify these errors, theoretical error estimates derived using information loss theory are first presented. Simulations are subsequently carried out in the canonical ensemble for various combinations of key parameters suggested by theoretical estimates. Numerically evaluated errors are compared to theoretical error estimates to assess whether the latter can qualitatively capture the loss of information during coarse-graining. Finally, a standing wave example is presented to illustrate how these error estimates can be used to control accuracy in CG-KMC by employing adaptive meshes.