Hidden Markov models have been used in the study of single-channel recordings of ion channel currents for restoration of idealized signals from noisy recordings and for estimation of kinetic parameters. A key to their effectiveness from a computational point of view is that the number of operations to evaluate the likelihood, posterior probabilities, and the most likely state sequence are proportional to the product of the square of the dimension of the state space and the length of the series. However, when the state space is quite large, computations can become infeasible. This can happen when the record has been low pass filtered and when the noise is colored. In this paper we present an approximate method that can provide very substantial reductions in computational cost at the expense of only a very small error. We describe the method and illustrate through examples the gains that can be made in evaluating the likelihood.