Electrostatically operated micro- and nanoelectromechanical (MEM/NEM) relays have been proposed as digital switches to replace transistors due to their sharp turn-on/off transient, zero leakage current between drain and source in the OFF-state, and capability to operate at far higher temperatures and radiation levels than CMOS. However, the different components associated with energy consumption in MEM/NEM relays, including the dynamic energy associated with charging the gate capacitance and static energy lost through substrate leakage, have not been investigated to date. Here, we present a detailed analysis of the energy consumption of NEM/MEM relays starting from first principles and compare against measurements carried out on silicon MEM relay prototypes. The dynamic energy consumed by a transistor in a binary switching transfer is accurately captured by 0.5CV2. This expression, which has also been used for relays, is only valid under the approximation of an unvarying capacitance C. However, the gate capacitance of an MEM/NEM relay varies as a function of gate voltage, as it is determined by the airgap between the gate electrode and the moving beam. We show how including this effect adds an extra term to the dynamic energy consumption expression. Furthermore, we investigate different current leakage mechanisms and devise a new method to estimate the substrate leakage current based on using the switching hysteresis of relays. The models, analyses, and measurement methodologies presented here constitute a set of essential techniques for accurate estimation of the energy consumption of MEM/NEM relays in ultralow power circuit applications.