We present two configurations for analog 0 to 2π optical phase modulation using liquid crystals (LCs), each of which achieve switching times that are 1 ms or less. One configuration is based on the switching behavior of a so-called nematic pi cell, and the other is based on the flexoelectro-optic effect in chiral nematic LCs when operated in the uniform lying helix geometry. Both configurations exploit a multipass optical arrangement to enhance the available optical phase range, while maintaining a fast switching speed. Moreover, these devices can be operated at or close to room temperature. Experimental data are found to be in good agreement with results predicted from theory for these multipass phase-modulation configurations.