We have studied the phenomenon of squeeze film damping in a liquid with a microfabricated vibrating plate oscillating in its fundamental mode with out-of-plane motion. It is paramount that this phenomenon be understood so that proper choices can be made in terms of sensor design and packaging. The influences of plate-wall distance $h$, effective plate radius $R$, and fluid viscosity and density on squeeze film damping have been studied. We experimentally observe that the drag force is inertia dominated and scales as $1/h3$ even when the plate is far away from the wall, a surprising but understandable result for a microfluidic device where the ratio of $h$ to the viscous penetration depth is large. We observe as well that the drag force scales as $R3$, which is inconsistent with squeeze film damping in the lubrication limit. These two cubic power laws arise due to the role of inertia in the high frequency limit.