While the primary concern for surveys using opt-in Internet panels is possible bias from self-selection, variance estimates are still useful regardless of whether the estimates are unbiased. Consistent asymptotic variance estimates can be obtained under weak conditions. These are compared to empirical estimates of sampling variability, along with estimates of the components of mean square error due to bias and sampling variability. The results are also applicable to other types of non-probability samples, such as low-response telephone polls.