Effects of sea-level rise (SLR) on future peak water levels in tidal deltas and estuaries are largely unknown, despite these areas being densely populated and at high risk of flooding. While the rates of SLR accelerate, many channels simultaneously experience channel deepening for navigation. With globally decreasing sediment supplies, most channels are at risk of becoming deeper when the rate of SLR accelerates and sedimentation cannot keep pace with SLR. These factors potentially favor amplification of the tides and thereby increase flood risk, but the extent to which they will do so is unknown. Here, we introduce and use a validated model for an artificially deepened multi-branch delta to get a mechanistic understanding of non-linear SLR-effects on peak water levels. Results show that, when the current deepened bed level will be maintained, peak water levels do not rise on par with mean sea-level. Thus flood risk increases less than what can be expected from the predictions of the mean sea-level increase. The reason is that SLR causes a proportional reduction in convergence of channel area. This mechanism reduces tidal amplification. Nevertheless, SLR effects extend far beyond the range of present-day seasonal variations, with future low water levels being equal to present-day high water levels, while the tidal range slightly reduces. This will have consequences not only for flood risk, but also for freshwater availability, navigation and ecology.