While a new type of oscillating-cup viscometer which uses a rotating magnetic field has been developed and tested, the uncertainty of such measurements has been considered to only a cursory level. This paper reports work in which the sensitivities of this new method's output are studied for the measurement of mercury with a particular device. It is concluded from the analysis that while the new method requires dramatically shorter measurement times than previous methods, the resultant uncertainty seems to be nearly the same as the classical oscillating cup method. As such, since the results are just as precise as other oscillating-cup methods, the new method should be employed for its speed advantage, allowing the viscosity of materials as functions of temperature or pressure to be economically determined.