Typical electromyogram (EMG) amplitude estimators use a fixed window length for smoothing the amplitude estimate. When the EMG amplitude is dynamic, previous research suggests that varying the smoothing length as a function of time may improve amplitude estimation. This paper develops optimal time-varying selection of the smoothing window length using a stochastic model of the EMG signal. Optimal selection is a function of the EMG amplitude and its derivatives. Simulation studies, in which EMG amplitude was changed randomly, found that the "best" adaptive filter performed as well as the "best" fixed-length filter. Experimental studies found the advantages of the adaptive processor to be situation dependent. Subjects used real-time EMG amplitude estimates to track a randomly-moving target. Perhaps due to task difficulty, no differences in adaptive versus fixed-length processors were observed when the target speed was fast. When the target speed was slow, the experimental results were consistent with the simulation predictions. When the target moved between two constant levels, the adaptive processor responded rapidly to the target level transitions and had low variance while the target dwelled on a level.