Marine- and lake-terminating glaciers, though limited in number, are important contributors to global sea-level rise. Their mass budget is governed by surface mass balance and frontal ablation. The latter remains poorly constrained in glacier models as calving involves processes that act on various spatial and temporal scales. In this manuscript, we present the integration of a subgrid-scale ice-front tracking method based on the level-set method, coupled with a strain-based calving criterion, into the Instructed Glacier Model. The framework is applied to a synthetic glacier setup initially to exemplify code sanity, reversibility, and shape preservation. For this experiment, the integration of both a re-initialization scheme and an informed extrapolation of frontal velocities was key. We also extended the approach to allow for frontal advance of grounded ice tongues. To further enhance the approach, we incorporated a thickness scheme that dynamically adjusts the frontal thickness, permitting the frontal advance of grounded ice tongues while maintaining consistency with mass conservation throughout geometric evolution. The framework is subsequently applied to a real-world setting, where the model is calibrated and evaluated using five marine-terminating glaciers in Kongsfjorden, Svalbard. The results show that the model can capture both the magnitude and spatial variability of calving front retreat. We therefore deem our implementation as a versatile method to track ice fronts of grounded glacier tongues. This scheme enables an adequate quantification of atmospheric and oceanic influences on current and future ice loss of marine-terminating glaciers.