Description of the physical behavior of electric guitars is still not very widespread in the scientific literature. In particular, the physical models describing a nonlinear behavior of pickups still requires some refinements. The study presented in this paper is focused on nonlinear modeling of the pickups. Two main issues are raised. First, is the currently most used nonlinear model (a Hammerstein model) sufficient for the complex nonlinear behavior of the pickup? In other words, would a more complex model, such as a Generalized Hammerstein that can deal better with the nonlinear memory, yield better results? The second troublesome issue is how to measure the nonlinear behavior of a pickup correctly. A specific experimental setup allowing for driving the pickup in a controlled way (string displacement perpendicular to the pickup) and to separate the nonlinear model of the pickup from other nonlinearities in the measurement chain is proposed. Thanks to this experimental setup , a Generalized Hammerstein model of the pickup is estimated for frequency range 15-500 Hz and the results are compared with a simple Hammerstein model. A comparison with experimental results shows that both models succeed in describing the pickup when used in realistic conditions.