In order to determine a guaranteed upper bound for worst case “1-cosine” gust loads of flexible aircrafts, the usage of the worst case energy-to-peak gain of linear parametervarying (LPV) systems has been recently proposed. A limitation of this approach is that it cannot deal with nonlinearities. This paper uses integral quadratic constraints (IQCs) to circumvent this restriction and to consider the saturation of a gust loads alleviation system. Based on the dissipation inequality framework, a linear matrix inequality constraint which bounds the worst case energy-to-peak gain of saturated LPV systems is given. In order to reduce the conservatism, an iterative procedure to refine local IQCs is proposed. The conservatism of this approach is analyzed at the example of a two-dimensional thin airfoil in combination with a saturated gust loads alleviation system.