We study, experimentally and theoretically, quantum weak localization (WL) corrections to the classical magnetoconductivity of two-dimensional ballistic systems with regular and disordered patterns of dense antidots. We analyze the observed temperature and flux dependences of the WL. using different theoretical models for the chaotic dynamics and dephasing rates. The measured resistivity curves, which deviate from those of diffusive systems, reflect chaotic motion and correlations in the classical dynamics of electrons in the antidot landscape. The results support the significance of the Ehrenfest time as a relevant time scale for ballistic WL. PACS numbers: 72.15.Rn, 05.45.Mt, 73.23.-b.