We consider estimates of the parameters of GARCH models of daily financial returns, obtained using intra-day (high-frequency) returns data to estimate the daily conditional volatility.Two potential bases for estimation are considered. One uses aggregation of high-frequency Quasi- ML estimates, using aggregation results of Drost and Nijman (1993). The other uses the integrated volatility of Andersen and Bollerslev (1998), and obtains coefficients from a model estimated by LAD or OLS, in the former case providing consistency and asymptotic normality in some cases where moments of the volatility estimation error may not exist. In particular, we consider estimation in this way of an ARCH approximation, and obtain GARCH parameters by a method related to that of Galbraith and Zinde-Walsh (1997) for ARMA processes. We offer some simulation evidence on small-sample performance, and characterize the gains relative to standard quasi-ML estimates based on daily data alone.