Micropolar field theories provide a systematic approach to modeling traditional materials like elastic bodies or viscous fluids that have microstructure. The downside to accounting for the behavior on the smaller scale is the introduction of many new parameters into the field equations. The difficulty of handling these new parameters can be mitigated by performing a sensitivity analysis to determine which parameters have the greatest impact on the solutions to the field equations. The sensitivity of an incompressible micropolar Stokes fluid to variations in the viscosity coefficients and boundary value of the microinertia is examined. This particular choice of field equations is motivated by an application of micropolar field theories to the deformation of the continental lithosphere, but the same approach can be used for other micropolar equations modeling solids or other types of fluids.