Invasive rodents pose significant ecological, economic, and public health challenges. Robust methods are needed for estimating population abundance to guide effective management. Traditional methods such as capture-recapture are often impractical for invasive species due to ethical, legal and logistical constraints. Here, the application of hierarchical multinomial N-mixture models for estimating the abundance of invasive rodents using removal data is highlighted. Firstly, a simulation study was performed which demonstrated minimal bias, as well as good precision and reliable coverage of confidence intervals across a range of sampling scenarios. Additionally, the consequences of violating the population closure assumption were illustrated by showing how between-occasion dynamics can bias inference. Secondly, removal data was analyzed for two invasive rodent species, namely coypus (Myocastor coypus) in France and muskrats (Ondatra zibethicus) in the Netherlands. Using hierarchical multinomial N-mixture models, the effect of temperature on abundance was examined, while accounting for imperfect and time-varying capture probabilities. Additionally, this study demonstrated how to accommodate spatial variability using random effects, quantify uncertainty in parameter estimates, and account for violations of closure by fitting an open-population model to multi-year data. Taken together, these approaches demonstrate the flexibility and utility of hierarchical models in invasive species management.