Boundary conditions at the frontal margins of tidewater glaciers provide important constraints on the balance of forces affecting ice flow and iceberg calving. For many large outlet glaciers in Greenland, the type of boundary condition (floating vs grounded ice) is not well known, owing to limited knowledge of ice thickness and fjord bathymetry. Here, we use high-rate GPS measurements collected at sites within a few km of the calving fronts of Kangerdlugssuaq and Helheim glaciers to examine the effect of ocean tide on ice flow. Data were collected at 5-15 s sampling rate during several campaign periods of 2-5 days in July 2005, and June, July and August 2006. The data were post-processed using a Kalman predictive filter to yield epoch-by-epoch station positions and elevations. Modeled ocean tides are shown to have good agreement with the tide stage measured over ~~3 weeks in July-August 2006 in Sermilik fjord, close to the terminus of Helheim Glacier. An analysis of ice vertical displacement and modeled ocean tide for Kangerdlugssuaq Glacier indicates the calving terminus was likely at near-flotation in July 2005. A tidal amplitude of ~~2.5 m produced an uplift of ~~2 m, and there was a detectable tidally-modulated variation in horizontal flow speed. Maximum uplift of the glacier was in phase with high tide. The absence of a lag indicates that the glacier tongue was responding to tidal height, and not to a progressive pressurization of the subglacial drainage system. Helheim Glacier also appears to have a short floating tongue, based on an analysis of GPS data collected in June-August 2006 at several stations located at increasing distances from the calving front. Glacier uplift was in phase with measured and modeled tidal height, but attenuated rapidly beyond ~~1 km from the terminus. We use the distribution of uplift signals to estimate the summer 2006 grounding line position. The ocean tide also caused noticeable variations in the down-glacier and across-glacier components of horizontal velocity, providing insight into grounding line conditions.