Nuclear magnetic resonance is used to measure the temperature dependence of the rotational viscosity coefficient, γ1, in the nematic phase of the compounds n-p-cyanobenzilidene-p-n-octyloxyaniline (CBOOA) and in 4-n-butoxybenzylidene-4'-n-heptylaniline (40-7). In this method pulsed NMR is used to observe the recovery of the nematic director following a sudden shift in the direction of an applied magnetic field. At temperatures far removed from the smectic A transition, the temperature dependence of the viscosity is compared to the microscopic theory of Martins with favorable agreement. Near the smectic A transition the divergence of γ1 is fitted to (T - Tc)-ν. Using Martins theory for the background viscosity in this region the exponent ν was determined to be 0.4 ± 0.1