Empirical researchers often estimate spillover effects by fitting linear or non-linear regression models to sampled network data. Here, we show that common sampling schemes induce dependence between observed and unobserved spillovers. Due to this dependence, spillover estimates are biased, often upwards. We then show how researchers can construct unbiased estimates of spillover effects by rescaling using aggregate network statistics. Our results can be used to bound true effect sizes, determine robustness of estimates to missingness, and construct estimates when missingness depends on treatment. We apply our results to re-estimate the propagation of idiosyncratic shocks between US public firms, and peer effects amongst USAFA cadets.