For estimating the realized volatility and covariance by using high frequency data, Kunitomo and Sato (2008a, b) have proposed the Separating Information Maximum Likelihood (SIML) method when there are micro-market noises. The SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic normality (or the stable convergence in the general case) when the sample size is large under general conditions with non-Gaussian processes or volatility models. We show that the SIML estimator has the robustness properties in the sense that it is consistent and has the asymptotic normality when there are micro-market (non-liner) adjustments and the round-off errors on the underlying stochastic processes.