Robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two-stage cluster sample in which the first-stage sampling fraction is small. The analysis is based on prediction (superpopulation) models that allow for very general correlation structure within clusters. Results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters. Ratio, regression, and mean-of-ratios statistics are in the class of population total estimators considered.