The history of sea level across the Quaternary is essential for assessing past and future climate. Global sea-level reconstructions are typically derived from oxygen isotope curves, but require calibration with geological constraints that are scarce prior to the last glacial cycle (>130 thousand years ago). Here we show that the coral reef terrace sequence at the Huon Peninsula (Papua New Guinea) provides such constraints up to ∼420 thousand years ago, through a geometric analysis of high-resolution topographic data. We derive a northward tectonic tilt as regional deformation pattern, and estimate relative sea level for 31 Quaternary periods, including several periods for which no relative sea level data exists elsewhere. Supported by numerical reef models, these estimates suggest that oxygen isotope-based global mean sea-level curves systematically underestimate interstadial sea-level elevations, by up to ∼20 m. Compared to those curves, our results imply a stronger degree of non-linearity between ice-sheet volumes and global temperatures within Quaternary glacial cycles.