Neural networks (NNs) are increasingly used for data-driven subgrid-scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non-linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large-amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN-based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics-based gravity wave (GW) parameterizations as a test case. WACCM has complex, state-of-the-art parameterizations for orography-, convection-, and front-driven GWs. Convection- and orography-driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto-encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO2). However, their performance is significantly improved by applying transfer learning, for example, re-training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data-driven parameterizations for various processes, including (but not limited to) GWs.