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Under the key assumption of finite $\rho$-variation, $\rho \in [1,2)$, of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), $\rho =1$ resp. $\rho =1/\left(2H\right)$, we recover and extend the respective results of ( (2009) 2689–2718) and ( (2012) 518–550). In particular, we establish an a.s. rate $k^{-(1/\rho -1/2-\epsilon )}$, any $\epsilon gt;0$, for Wong–Zakai and Milstein-type approximations with mesh-size...