Propagation of waves of biochemical activities through consecutive stages of the cell cycle is essential to execute the steps of cell division in a strict temporal order. Mechanisms that ensure the proper amplitude and timing of these waves are poorly understood. Using a synthetic gene circuit, we show that a transcriptional activator driven by yeast cell-cycle promoters propagates transcriptional oscillations with substantial damping. Although regulated nuclear translocation has been implicated in the timing of oscillatory events, mathematical analysis shows that increasing the rate of nuclear transport is an example of a general regulatory principle, which enhances the fidelity of wave propagation. Indeed, increasing the constitutive import rate of the activator counteracts the damping of waves and concurrently preserves the intensity of the signal. In contrast to the regulatory range of nuclear transport, the range of mRNA turnover considerably limits transcriptional wave propagation. This classification of cellular processes outlines potential regulatory mechanisms that can contribute to faithful transmission of oscillations at different stages of the cell cycle.