This paper considers conditional heteroskedasticity-robust testing for cointegration in nonstationary vector autoregressive models under conditional heteroskedasticity. The likelihood ratio (LR) cointegration tests of Johansen (1988, 1991) assume the Gaussian independent and identically distributed innovations, and hence the stylized facts of time-variant and persistent volatility may affect the performance of the tests. In this paper, we allow for conditionally heteroskedastic innovations and formulate the Wald test statistics. The asymptotic distribution of the Wald tests is shown to follow the nonstandard distribution. The simulation evidence regarding the performance of the proposed tests demonstrates robustness to persistent conditional volatility.