Flow in a planar cavity bounded by stationary side walls, a flat gas/liquid interface covered by an insoluble monolayer, and driven by sinusoidal motion of the floor is examined numerically. Navier-Stokes computations with the Boussinesq-Scriven surface model are presented utilizing the equation-of-state measured for a vitamin KI monolayer on the air/water interface. The results identify a range of initial surfactant concentration for which the surface velocity is sensitive to the surface viscosity B (sum of surface shear and dilatational viscosities) down to 10(-2) surface Poise. Thus, the study suggests a practical method for determining surface viscosities consisting of the measurement of the motion of a tracer particle on the interface and comparisons with numerical computations at various values of B.