The history of sea level across the Quaternary is essential for assessing past and future climate and geodynamics. Global sea-level reconstructions are typically derived from oxygen isotope curves, but require calibration with geological constraints that are particularly scarce prior to the last glacial cycle (>130 ka). The exceptionally well-preserved coral reef terrace sequence in the Huon Peninsula (Papua New Guinea) may provide such constraints up to ~420 ka, but has never been analysed in its full extent, or with high-resolution topographic data. Here we apply novel geometric approaches to show that the terrace sequence deformation pattern can be approximated by a northward tectonic tilt, and estimate relative sea-level (RSL) for 31 Late Pleistocene periods, including several periods for which no other RSL data exists elsewhere. Supported by reef modelling, these estimates suggest that global mean sea-level curves derived from oxygen isotopes systematically underestimate interstadial sea-level elevations, by up to ~20m. We propose that this discrepancy is either an effect of incorrect oxygen isotope curve calibrations, or that some short-lived sea-level variations are simply not recorded in oxygen isotope ratios.