Exploitation rates are often estimated using tag‐return studies. However, in fisheries with a catch‐and‐release component, exploitation rate or fishing mortality may not be the most important metric of interest. Instead, angler catch rates (e.g., fish caught per hour), total catch (including fish that are harvested or released), or the average number of times an individual fish is caught may be a better measure of fishery performance. However, if anglers remove tags from fish before release, then catch estimates will be negatively biased because tag removal will not be accounted for. In this study, maximum likelihood estimation methods were used to estimate catch in fisheries with high rates of catch and release. Right‐censored models were used to accommodate tags that may or may not be removed by anglers. Model‐derived maximum likelihood estimates of mean catch were relatively unbiased under two simulated fishery scenarios. There was a nonlinear, positive relationship between the percentage of tags that were removed from fish before release and the standard error of estimated mean catch. Although the models performed well at estimating catch in the simulations, more study is needed to evaluate how possible violation of model assumptions can affect catch estimates.