Microperforated plates (MPP) are traditionally used in sound control technologies to advantageously absorb acoustic waves. However, little is known concerning the additional structural damping they can induce through exchanges in the viscous and thermal boundary layers near the fluid-structure interface of the microperforations. MPP therefore offer an alternative to, or can be used together with, viscoelastic materials, commonly implemented to damp vibrations at medium and high frequencies. In this work, the structural damping capabilities of finite MPP are investigated. First, an analytical model is developed using an alternative form of the Biot model, classically devoted to porous plates, involving energy dissipation through viscous friction mechanisms. The analytical results are compared to experimental measurements of structural damping factors on various MPP samples. The model is validated and confirms the damping effect added by the microperforations in the low frequency range. A sensitivity analysis on perforation rate and perforation diameter provides a characteristic frequency that when coinciding with a plate natural frequency maximizes the added damping.