Ordinary kriging is well-known to be optimal when the data have a multivariate normal distribution (and if the variogram is known), whereas lognormal kriging presupposes the multivariate lognormality of the data. But in practice, real data never entirely satisfy these assumptions. In this article, the sensitivity of these two kriging estimators to departures from these assumptions and in particular, their resistance to outliers is considered. An outlier effect index designed to assess the effect of a single outlier on both estimators is proposed, which can be extended to other types of estimators. Although lognormal kriging is sensitive to slight variations in the sill of the variogram of the logs (i.e., their variance), it is not influenced by the estimate of the mean of the logs.