We introduce a blocking and regularization approach to estimate high-dimensional covariances using high-frequency data. Assets are first grouped according to liquidity. Using the multivariate realized kernel estimator of Barndorff-Nielsen et al. (2010), the covariance matrix is estimated block-wise and then regularized. The performance of the resulting blocking and regularization (?RnB?) estimator is analyzed in an extensive simulation study mimicking the liquidity and market microstructure features of the S&P 1500 universe. The RnB estimator yields efficiency gains for varying liquidity settings, noise-to-signal ratios and dimensions. An empirical application of estimating daily covariances of the S&P 500 index confirms the simulation results.