Mapping modern and paleo-grounding lines around the Antarctic Ice Sheet elucidates processes occurring at the grounded ice-ocean interface. Positional differences across individual grounding lines manifest as longitudinal (plan-view) grounding line sinuosity. We explore the causes and significance of such sinuosity by coupling observations of contemporary Antarctic grounding lines and paleo-grounding lines expressed as ice-marginal landforms, specifically focusing on the role that bed topography may play in influencing grounding-line sinuosity. For equal-length grounding-line segments, modern and paleo-grounding lines have remarkably similar sinuosity distributions, with the vast majority of grounding lines being near linear. Surprisingly, grounding line sinuosity is highest on low sloping beds and lower on rougher beds, even for grounding lines that are clearly pinned on topographic highs. For contemporary grounding lines, sinuosity is higher and more variable for grounding lines near floatation with shallow height-above-buoyancy gradients. We argue that grounding line sinuosity is a product of the combined influence of height-above-buoyancy gradient, bed slope, and bed roughness and, perhaps counterintuitively, that this relationship does not appear to be sensitive to the presence of pinning points, ice-flow speed, or the presence/absence of an ice shelf.