An effective method has been developed to calculate the sensitivity of the resonance peak frequency and forced response level to variation of parameters of nonlinear friction contact interfaces and excitation. The method allows determination of the sensitivity characteristics simultaneously with the resonance peak frequency and response level calculated as a function of any parameter of interest and without significant computational expense. Capabilities of the method are demonstrated on examples of analysis of large-scale finite element models of realistic bladed disks with major types of the nonlinear contact interfaces: (i) a blisk with underplatform dampers, (ii) a bladed disk with friction damping at blade fir-tree roots, and (iii) a high-pressure bladed disk with shroud contacts. The numerical investigations show high efficiency of the method proposed.