In linear regression models estimated by ordinary least squares, it is often desirable to use hypothesis tests and confidence intervals that remain valid in the presence of heteroskedastic errors. Wald tests based on heteroskedasticity-consistent covariance matrix estimators (HCCMEs, also known as sandwich estimators or simply "robust" standard errors) are a well known and widely applied method that remains asymptotically valid under heteroskedasticity of an unspecified form. Wald-type t-tests based on HCCMEs maintain nominal rejection rates when the sample size is large, but they are not always accurate with small samples; moreover, it can be difficult to determine whether a given sample is large enough to trust the asymptotic approximation. This paper reviews several approaches to approximating the null sampling distribution of HCCME t-tests and thereby improving the accuracy of rejection rates in small samples. Using simulations, we investigate the relative performance of Satterthwaite, Edgeworth, and saddlepoint approximations under a wide range of data generating processes. Results indicate that certain distributional approximations perform similarly to conventional tests based on HCCMEs, and can improve upon them when the nominal Type-I error rate is less than 0.05.