We consider frictional contact problems in small strain elasticity discretized with finite elements and Nitsche method. Both bilateral and unilateral contact problems are taken into account, as well as both Tresca and Coulomb models for the friction. We derive residual a posteriori error estimates for each friction model, following [Chouly et al, IMA J. Numer. Anal. (38) 2018, pp. 921-954]. For the incomplete variant of Nitsche, we prove an upper bound for the dual norm of the residual, for Tresca and Coulomb friction, without any extra regularity and without a saturation assumption. Numerical experiments allow to assess the accuracy of the estimates and their interest for adaptive meshing in different situations.