Ocean tides under the large Weddell Sea ice shelves are among the least well observed on Earth. Here we present new, spatially extensive observations of the vertical tidal motion of the Filchner-Ronne and Larsen C ice shelves using Global Positioning System (GPS) data spanning a few weeks to years. We pay particular attention to the major tidal constituents (M2, S2, O1, K1) as well as important GRACE aliasing periods (K2 and S1). We compare the estimated constituents with recent global and regional tide models and find that no single model is the most accurate across all constituents or ice shelves. The root-sum-square errors are 7-8 cm (CATS2008a and TPXO7.2) and 11-12 cm (GOT4.7 and FES2004) with the energetic M2 (RMSE = 4-8 cm) and S2 (4-5 cm) generally dominating these statistics. The FES2004 K1 is particularly inaccurate near the Larsen C Ice Shelf, with errors approaching 20 cm, meaning that GRACE Release 4 estimates of mass change in the northern Antarctic Peninsula will be biased. We find tidal energy at 3, 4, 5, 6 and, weakly, at 7 cycles per day at all of our sites. The largest amplitudes within these bands are at M4, MO3 and SP3 and approach 30 mm, although significant spatial variations exist. We show that they generally do not appear to originate in areas of reduced water column in ice shelf grounding zones. Comparing model estimates with our M4, MS4 and MN4 values shows that models do not accurately represent these terms.