For the fatigue life of thin-walled components, not only fatigue crack initiation, but also crack growth is decisive. The phase-field method for fracture is a powerful tool to simulate arbitrary crack phenomena. Recently, it has been applied to fatigue fracture. Those models pose an alternative to classical fracture-mechanical approaches for fatigue life estimation. In the first part of this paper, the parameters of a phase-field fatigue model are calibrated and its predictions are compared to results of fatigue crack growth experiments of aluminium sheet material. In the second part, compressive residual stresses are introduced into the components with the help of laser shock peening. It is shown that those residual stresses influence the crack growth rate by retarding and accelerating the crack. In order to study these fatigue mechanisms numerically, a simple strategy to incorporate residual stresses in the phase-field fatigue model is presented and tested with experiments. The study shows that the approach can reproduce the effects of the residual stresses on the crack growth rate.