© 2017, Springer International Publishing AG. Residual-type a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter. The case of the Dirichlet boundary conditions was considered in the recent article (Kopteva, Numer. Math., 2017, Published online 2 May 2017. doi:10.1007/s00211-017-0889-3). Now we extend this analysis to also allow boundary conditions of Neumann type.