Oscillating droplet experiments are conducted using the Electromagnetic Levitation (EML) facility under microgravity conditions. The droplet of molten metal is internally stirred concurrently with the pulse excitation initiating shape oscillations, allowing viscosity measurement of the liquid melts based on the damping rate of the oscillating droplet. We experimentally investigate the impact of convection on the droplet’s damping behavior. The effective viscosity arises and increases as the internal convective flow becomes transitional or turbulent, up to 2–8 times higher than the intrinsic molecular viscosity. The enhanced effective viscosity decays when the stirring has stopped, and an overshoot decay pattern is identified at higher Reynolds numbers, which presents a faster decay rate as the constraint of flow domain size becomes influential. By discriminating the impact of convection on the viscosity results, the intrinsic viscosity can be evaluated with improved measurement accuracy.