Contemporary research has begun to show a strong relationship between movements and the perception of time. More specifically, concurrent movements serve to both bias and enhance time estimates. To explain these effects, we recently proposed a mechanism by which movements provide a secondary channel for estimating duration that is combined optimally with sensory estimates. However, a critical test of this framework is that by introducing noise into movements, sensory estimates of time should similarly become noisier. To accomplish this, we had human participants move a robotic arm while estimating intervals of time in either auditory or visual modalities (n = 24, ea.). Crucially, we introduced an artificial tremor in the arm while subjects were moving, that varied across three levels of amplitude (1-3 N) or frequency (4-12 Hz). The results of both experiments revealed that increasing the frequency of the tremor led to noisier estimates of duration. Further, the effect of noise varied with the base precision of the interval, such that a naturally less precise timing (i.e., visual) was more influenced by the tremor than a naturally more precise modality (i.e., auditory). To explain these findings, we fit the data with a recently developed drift-diffusion model of perceptual decision-making, in which the momentary, within-trial variance was allowed to vary across conditions. Here, we found that the model could recapitulate the observed findings, further supporting the theory that movements influence perception directly. Overall, our findings support the proposed framework, and demonstrate the utility of inducing motor noise via artificial tremors.