We study the estimation of familial correlations from pedigree data without the assumption of multivariate normality, using asymptotic results to obtain standard errors and confidence intervals. Two extreme weights that can be given to pairs of observations from relatives in pedigrees are pair-wise weights, in which each pair is given the same weight, and uniform weights, in which each pedigree is given the same weight. A best weighted average of these two estimates for a particular correlation as well as its standard error are derived using quadratic models for the estimates and their variances. Conclusions regarding the adequacy of the method in terms of bias, absolute bias, variance, and confidence interval coverage probabilities are presented on the basis of results from simulation studies. We determine under what circumstances the nominal 95 percent confidence intervals have excellent average coverage of the true values even for samples of small size and under what circumstances the results must be viewed with caution. We then describe a procedure by which, for both small family and large family structures, we find that the estimates we recommend provide accurate results.