Temporal variability in the partitioning of mass loss from the Greenland Ice Sheet suggests a complex response to recent climatic change. The contribution to sea level rise from tidewater glaciers is also spatially variable across the ice sheet, and observations reveal their contrasting behaviour at a regional scale. Whilst ice-ocean interaction may explain their dynamics in the south of Greenland, the warm subtropical waters responsible for this extend only to mid-latitudes. In this study, the geometric setting and bed condition is therefore investigated to better understand the flow characteristics and dynamics of high-latitude tidewater glaciers in Greenland. New ice thickness measurements are combined with a novel mass conservation method to reconstruct high resolution (<300 m) bed topographies for 4 tidewater glaciers in northern Greenland. A 3D inversion using control methods is then applied to each glacier with the full-stokes model, Elmer/Ice, to calculate basal drag. The bed topographies reveal that these glaciers are underlain by deeply incised channels, which extend more inland and descend further below present sea level than previously thought. The results of the inversions show spatially variable drag across the beds of these glaciers, but highlight a close relationship with local changes in bed elevation. This may be attributed to form drag by topographic highs, or the infilling of depressions with soft sediment and water. Regardless, the results of this study imply that these glaciers are far more vulnerable to future sea level rise than previously recognised, and may themselves contribute significantly to this in response to a relatively small, future perturbation.