Despite the accelerated deployment of laminated composites in a wide variety of markets due to their peculiar engineering features, the design of those materials is often restrained by the lack of cost-efficient modeling techniques. In fact, the existing strategies allowing for cheap simulations usually fail to directly capture out of-plane through-the-thickness stresses, which prove to be typically responsible of delamination failure modes. In this paper, we introduce a fast and accurate stress recovery strategy to model the out-of-plane behavior of Kirchhoff laminated plates. The proposed technique can be regarded as a two-step approach: First, the classical composite plates theory, providing the lowest computational cost among known literature strategies, is applied to obtain a coarse displacement solution; afterwards, this solution is used to compute the necessary in-plane derivatives to recover the out-of-plane stresses directly imposing equilibrium in strong form. Since this a posteriori step relies on high-order in-plane continuity requirements, isogeometric analysis (IGA) represents a natural simulation framework given its accuracy and higher continuity properties. Both isogeometric Galerkin and collocation formulations are herein considered. The effectiveness of the proposed approach is proven by extensive numerical tests.