Abstract <p>This work addresses the geometric parametrization of dynamic linear sloshing simulations using: (i) isogeometric analysis (IGA), (ii) projection-based reduced-order model (PROM) with proper orthogonal decomposition (POD), and (iii) energy-conserving sampling and weighting (ECSW). The originality of the approach lies in the combination of these three methods to generate parameterized, non-affine reduced-order models on a reference configuration, enabling the prediction of the dynamic behavior of free-surface liquids across various geometrical configurations. The proposed methodology involves generating a projection basis and a reduced-order model from <i>off-line</i> time integration simulations. This PROM enables fast and reliable parameterized <i>on-line</i> response evaluations of liquid pressure in the time domain under prescribed accelerations. Numerical examples demonstrate the speed-up and accuracy of the reduced-order model compared to the high-dimensional model.</p> Graphic abstract <p></p>