The Nonlinear Schr¨odinger equation can be derived as an amplitude equation describing slow modulations in time and space of an underlying spatially and temporarily oscillating wave packet. It is the purpose of this paper to prove estimates, between the formal approximation, obtained via the Nonlinear Schr¨odinger equation, and true solutions of the original system in case of non-trivial quadratic resonances. It turns out that the approximation property holds if the approximation is stable in the system for the three wave interaction associated to the resonance. It does not hold if instability occurs for the approximation in this system. Although we restrict ourselves to a nonlinear wave equation as original system we believe that this is a general result. A consequence of the result is the long time existence of modulated waves in case of stable resonances and blow up of modulated waves in case of an unstable resonance.