Measurement of a solution’s viscosity is an important analytic technique for a variety of applications including medical diagnosis, pharmaceutical development, and industrial processing. The use of droplet-based (e.g., water-in-oil) microfluidics for viscosity measurements allows nanoliter-scale sample volumes to be used, much smaller than those either in standard macro-scale rheometers or in single-phase microfluidic viscometers. By observing the flow rate of a sample plug driven by a controlled pressure through an abrupt constriction, we achieve accurate and precise measurement of the plug viscosity without addition of labels or tracer particles. Sample plugs in our device geometry had a volume of ∼30 nL, and measurements had an average error of 6.6% with an average relative standard deviation of 2.8%. We tested glycerol-based samples with viscosities as high as 101 mPa s, with the only limitation on samples being that their viscosity should be higher than that of the continuous oil phase.