Depth-integrated (1-D) flowline models have been widely used to simulate fast-flowing tidewater glaciers and predict change because the continuous grounding line tracking, high horizontal resolution, and physically based calving criterion that are essential to realistic modeling of tidewater glaciers can easily be incorporated into the models while maintaining high computational efficiency. As with all models, the values for parameters describing ice rheology and basal friction must be assumed and/or tuned based on observations. For prognostic studies, these parameters are typically tuned so that the glacier matches observed thickness and speeds at an initial state, to which a perturbation is applied. While it is well know that ice flow models are sensitive to these parameters, the sensitivity of tidewater glacier models has not been systematically investigated. Here we investigate the sensitivity of such flowline models of outlet glacier dynamics to uncertainty in three key parameters that influence a glacier's resistive stress components. We find that, within typical observational uncertainty, similar initial (i.e., steady-state) glacier configurations can be produced with substantially different combinations of parameter values, leading to differing transient responses after a perturbation is applied. In cases where the glacier is initially grounded near flotation across a basal over-deepening, as typically observed for rapidly changing glaciers, these differences can be dramatic owing to the threshold of stability imposed by the flotation criterion. The simulated transient response is particularly sensitive to the parameterization of ice rheology: differences in ice temperature of ~ 2 °C can determine whether the glaciers thin to flotation and retreat unstably or remain grounded on a marine shoal. Due to the highly non-linear dependence of tidewater glaciers on model parameters, we recommend that their predictions are accompanied by sensitivity tests that take parameter uncertainty into account.