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Tide‐influenced deltas are among the largest depositional features on Earth and are ecologically and economically important as they support large populations. However, the continued rise in relative sea level threatens the sustainability of these landscapes and calls for new insights on their morphological response. While field studies of ancient deposits allow for insight into delta evolution during times of eustatic adjustment, tide‐influenced deltas are notoriously hard to identify in the rock record. We present a suite of physical experiments aimed at investigating the morphological response of tide‐influenced deltas subject to relative sea‐level rise. We show that increasing relative tidal energy changes the response of the delta because tides effectively act to remove fluvially deposited sediment from the delta topset. This leads to enhanced transgression, which we quantify via a new methodology for comparing shoreline transgression rates based on the concept of a ‘transgression anomaly’ relative to a simple reference case. We also show that stronger tidal forcing can create composite deltas where distinct land‐forming processes dominate different areas of the delta plain, shaping characteristic morphological features. The net effect of tidal action is to enhance seaward transfer of bedload sediment, resulting in greater shoreline transgression compared to identical, yet purely fluvial, deltaic systems that exhibit static or even regressive shorelines. © 2019 John Wiley & Sons, Ltd.