Here we describe development of a microfluidic viscometer based on arrays of magnetically actuated micro-posts. Quantitative viscosities over a range of three orders of magnitude were determined for samples of less than 20 μL. This represents the first demonstration of quantitative viscometry using driven flexible micropost arrays. Critical to the success of our system is a comprehensive analytical model that includes the mechanical and magnetic properties of the actuating posts, the optical readout, and fluid-structure interactions. We found that alterations of the actuator beat shape as parameterized by the dimensionless "sperm number" must be taken into account to determine the fluid properties from the measured actuator dynamics. Beyond our particular system, the model described here can provide dynamics predictions for a broad class of flexible microactuator designs. We also show how the model can guide the design of new arrays that expand the accessible range of measurements.