This article proposes the use of estimating functions based on composite likelihood for the estimation of isotropic as well as geometrically anisotropic semivariogram parameters. The composite likelihood approach is objective, eliminating the specification of distance lags and lag tolerances associated with the commonly used moment estimator. Extensions to the geometric anisotropy case include a parameterized transformed distance function, which eliminates the subjective estimation of the parameters of geometric anisotropy. The composite likelihood approach requires no matrix inversions and the estimators are shown to be consistent in a fashion similar to maximum likelihood and restricted maximum likelihood but without reliance on strong distributional assumptions. Predictions based on composite likelihood estimates performed very well using isotropic and geometric anisotropic simulated data and compared favorably to predictions based on the traditional approach in the isotropic case. Comparisons were also made using data collected on iron-ore measurements where previous analyses determined a geometric anisotropic semivariogram model to be appropriate.