Continuous inkjet devices require fast and reliable prediction of droplet formation to support design exploration and control. We consider a one-dimensional liquid-jet model for early-time breakup, formulated in terms of a cross-sectional area and axial momentum with capillary pressure and discretized on a periodic grid, following the classical analysis of drop formation in liquid jets by Lee [1]. The full-order model (FOM) is integrated by an explicit Runge–Kutta scheme whose time step is limited by nonlinear stability constraints associated with neck collapse. From pre-breakup snapshots of this reference simulation, we construct separate proper orthogonal decomposition (POD) bases for the area and momentum fields and apply a discrete empirical interpolation method (DEIM) hyper-reduction to the nonlinear momentum residual [2]. The resulting POD–DEIM reduced-order model (ROM) is assessed by time-domain comparisons and eigenvalue-based stability diagnostics. For the training case and an interpolated parameter set, the ROM tracks necking dynamics up to normalized times of about 0.99 of the breakup time with typical relative errors below 1% over most of this interval. As the neck radius approaches zero, the model becomes increasingly sensitive, and some trajectories diverge near the pinch-off event. At the same time, POD filtering reduces the Jacobian spectral radius, enlarging the admissible time step: configurations that are unstable in the FOM at a time step of 1.0×10^(-5) remain stable in the ROM, enabling a tenfold step-size increase and order-of-magnitude savings for early-time prediction. These results provide a quantitative baseline for projection-based reduced-order modeling of jet breakup and motivate the exploration of alternative time-discrete formulations that further enhance robustness near pinch-off.