Markovian models of ion channels have proven useful in the reconstruction of experimental data and prediction of cellular electrophysiology. We present the stochastic Galerkin method as an alternative to Monte Carlo and other stochastic methods for assessing the impact of uncertain rate coefficients on the predictions of Markovian ion channel models. We extend and study two different ion channel models: a simple model with only a single open and a closed state and a detailed model of the cardiac rapidly activating delayed rectifier potassium current. We demonstrate the efficacy of stochastic Galerkin methods for computing solutions to systems with random model parameters. Our studies illustrate the characteristic changes in distributions of state transitions and electrical currents through ion channels due to random rate coefficients. Furthermore, the studies indicate the applicability of the stochastic Galerkin technique for uncertainty and sensitivity analysis of bio-mathematical models.