We investigate the efficiency potential of organic-inorganic halide perovskite/crystalline silicon tandem solar cells, a new class of photovoltaic devices targeting long-term cost reductions by ultrahigh conversion efficiencies. Methyl ammonium lead triiodide perovskite solar cells are particularly interesting as the top cell in Si-based tandem devices due to their suitable band gap, high photovoltage, and low sub-bandgap absorption. We derive optical models for a perovskite/Si tandem cell with Lambertian light trapping in the perovskite top cell, as well as for a top cell in the single pass limit. We find that unlike for other thin-film device architectures, light trapping is not required for the triiodide perovskite/Si tandem to reach matched top and bottom cell currents. While a Lambertian top cell could be employed in a four-terminal tandem, a top cell in the single pass limit enables a current-matched monolithic device with realistic top cell thicknesses. We calculate a limiting efficiency of 35.67% for an ideal (no parasitic absorption, ideal contacts) monolithic tandem, assuming a top cell open-circuit voltage of 1100 mV.