The telecommunications industry follows a tendency towards smaller devices, higher power and higher frequency, which imply an increase on the complexity of the electronics involved. Moreover, there is a need for extended capabilities like frequency tunable devices, ultra-low losses or high power handling, which make use of advanced materials for these purposes. In addition, increasingly demanding communication standards and regulations push the limits of the acceptable performance degrading indicators. This is the case of nonlinearities, whose effects, like increased Adjacent Channel Power Ratio (ACPR), harmonics, or intermodulation distortion among others, are being included in the performance requirements, as maximum tolerable levels. In this context, proper modeling of the devices at the design stage is of crucial importance in predicting not only the device performance but also the global system indicators and to make sure that the requirements are fulfilled. In accordance with that, this work proposes the necessary steps for circuit models implementation of different passive microwave devices, from the linear and nonlinear measurements to the simulations to validate them. Bulk acoustic wave resonators and transmission lines made of high temperature superconductors, ferroelectrics or regular metals and dielectrics are the subject of this work. Both phenomenological and physical approaches are considered and circuit models are proposed and compared with measurements. The nonlinear observables, being harmonics, intermodulation distortion, and saturation or detuning, are properly related to the material properties that originate them. The obtained models can be used in circuit simulators to predict the performance of these microwave devices under complex modulated signals, or even be used to predict their performance when integrated into more complex systems. A key step to achieve this goal is an accurate characterization of materials and devices, which is faced by making use of advanced measurement techniques. Therefore, considerations on special measurement setups are being made along this thesis.