Ozone treatment is an effective barrier against viral pathogens, wherefore it is an integral part of many water and wastewater treatment trains. However, the efficacy of ozone treatment remains difficult to monitor, due to the lack of methods to track virus inactivation in real-time. The goal of this work was to identify easy-to-measure proxies to monitor virus inactivation during water and wastewater treatment by ozone. Proxies considered were the abatement in UV absorbance at 254 nm (UV) and carbamazepine (CBZ), a ubiquitous organic micropollutant with a similar abatement rate constant as human viruses. The proxies, as well as the inactivation of two viruses (MS2 coliphage and coxsackievirus B5) were measured in surface water and in a secondary wastewater effluent as a function of the specific ozone dose (mgO/mg dissolved organic carbon). Virus inactivation was rapid in both matrices, but was more efficient in surface water. This trend was also evident when inactivation was assessed as a function of the ozone exposure to account for the different ozone demand of the two water types. Both proxies, as well as the specific ozone dose, were correlated with virus inactivation. The correlations depended only weakly on the virus species, but - with the exception of CBZ abatement - differed between the two water types. Finally, predictive relationships were established using Bayesian power models, to estimate virus inactivation based on the measurement of a proxy. The models were then applied to estimate the MS2 inactivation in a pilot-scale ozone reactor that treats surface water of Lake Zurich. All proxies yielded good estimates of the actual MS2 inactivation in the pilot plant, indicating that the proxy-inactivation relationships established in the laboratory can also be applied to flow-through reactors. This study confirms that ozone is a highly effective disinfectant for viruses in both surface water and wastewater, and that the abatement of UV and CBZ can be used to track virus inactivation during water and wastewater treatment.