I am trying to fit a model to binomially distributed data, which I have done via the maximum likelihood method. Normally I'm working with normally distributed data (or data which I can convince myself and occasionally others is normally distributed) and I'm a little confused about how to find asymmetric errors on my parameters. Usually I find uncertainties by scanning the space of the fitted parameters and finding the surface where the X^2 is one greater than the best fit value. I have found some unproven statements suggesting that this method is applicable regardless of whether one is using Gaussian maximum likelihood or not. Is this the case?
What you're describing is the Method of Support, which relies on the asymptotic property of the likelihood ratio statistic L, namely that -2L is has an approximate chi-square distribution.
A more direct method is to use the second derivatives of the log-likelihood function to obtain the observed Fisher information matrix. The inverse of this matrix, evaluated at the point of maximum likelihood, is the estimated variance-covariance matrix for your model parameters.
I've had great success doing this in Mathematica, where the derivatives can be calculated on the fly without doing all the messy calculus by hand.