Observations in estuaries indicate that an amplified tidal wave moves considerably faster than is indicated by the classical equation for wave propagation. Similarly, the celerity of propagation is lower if the tidal wave is damped. This phenomenon is clearly observed in the Schelde estuary (located in the Netherlands and Belgium) and in the Incomati estuary in Mozambique. In the Incomati, the tidal wave is damped throughout, whereas in the Schelde the tidal range increases from the mouth until the city of Antwerp, after which it decreases until Gent. This paper derives a new analytical expression for the celerity of the tidal wave that takes into account the effect of tidal damping, as an expansion of the classical equation for tidal wave propagation. In the new equation the phase lag between high water and high water slack plays a crucial role. It is one of the main parameters determining tidal wave propagation in alluvial estuaries. The equation is successfully applied to observations in the Schelde and the Incomati.