This study presents a thorough theoretical and experimental investigation on the nonlinear damping of in-plane micromachined electromechanical resonators. More specifically, experiments are conducted on an electrically actuated bridge resonator and the primary resonance response of the system is obtained at various AC and DC voltages. A nonlinear theoretical model is developed using the Euler-Bernoulli beam theory while accounting for the geometric, electrostatic (including fringing field effect), and damping nonlinearities. Two damping models are considered in the theoretical model; the Kelvin-Voigt model, which for this system is a nonlinear damping model due to the presence of geometric nonlinearities. The second damping model consists of linear, quadratic, and cubic damping terms. A high-dimensional discretisation is performed, and the nonlinear dynamics of the resonator are examined in detail in the primary resonance regime by constructing the frequency response diagrams at various AC and DC voltages. Thorough comparisons are conducted between the experimental data and the theoretical results for different damping conditions. It is shown that the micro resonator displays strong nonlinear damping. Detailed calibration procedures for the nonlinear damping models are proposed and the advantages and disadvantages of each nonlinear damping model are discussed.