Social network analysis of animal societies allows scientists to test hypotheses about social evolution, behaviour, dynamical processes, and transmission events such as the spread of disease. However, the accuracy of estimated social network metrics depends on the proportion of individuals sampled, actual sample size, and frequency of observations. Robustness of network metrics derived from a sample has thus far been examined through various simulation studies. However, simulated data do not necessarily reflect the nuances of real empirical data. We used some of the largest available GPS telemetry relocation datasets from five species of ungulates characterised by different behavioural and ecological traits and living in distinct environmental contexts to study the bias and robustness of social network metrics. We introduced novel statistical methods to quantify the uncertainty in network metrics obtained from a partial population suited to autocorrelated data such as telemetry relocations. We analysed how social network metrics respond to down-sampling from the observed data and applied pre-network data permutation techniques, a bootstrapping approach, correlation, and regression analyses to assess the stability of network metrics when based on samples of a population. We found that global network metrics like density remain robust when the sample size is lowered, whereas some local network metrics, such as eigenvector centrality, are entirely unreliable when a large proportion of the population is not monitored. We show how to construct confidence intervals around the point estimates of these metrics representing the uncertainty as a function of the number of nodes in the network. Our uncertainty estimates enable the statistical comparison of social network metrics under different conditions, such as analyzing daily and seasonal changes in the density of a network. Despite the striking differences in the ecology and sociality among the five different ungulate species, the various social network metrics behave similarly under down sampling, suggesting that our approach can be applied to a wider range of species across vertebrates. Our methods can guide methodological decisions about animal social network research (e.g., sampling design and sample sizes) and allow more accurate ecological inferences from the available data.