The accurate prediction of absorption energies is a prerequisite for effective molecular and materials design in many applications, such as in biomedical imaging and organic electronics. The near-infrared (NIR) region of the electromagnetic spectrum is of particular interest for biomedical imaging, but this region also presents unique challenges for many existing physics-based and machine learning prediction methods. These challenges stem from a variety of sources, but a thorough investigation of these shortcomings has previously not been possible due to the lack of large datasets available in this area. In this work, we extracted experimental measurements from the literature for >4,600 unique chromophore-solvent pairs that absorb or emit in the NIR, and we used this data to benchmark a variety of physics-based calculations and state-of-the-art deep learning architectures. We found that even relatively expensive physics-based calculations such as range-separated hybrid time-dependent density functional theory have major failures in trying to approximate experimental values in the NIR, but these errors are largely systematic and improve with calibration by simple linear regression. While several machine learning methods have recently excelled at predicting UV/Vis optical properties, we found that these methods performed substantially worse on NIR absorption prediction. This is partially due to the greater dependence of NIR properties on long-range effects in molecular structure (and the difficulty graph-based models have with communicating long-range information). However, we show that providing additional NIR data to simpler models increases predictive accuracy more than using more complex models to incorporate long-range information. Machine learning models outperformed calibrated physics-based calculations on predictions in the NIR region when the machine learning models were trained on sufficient NIR data. Overall, this work shows the promise and limitations of physics-based and data-driven approaches for predicting NIR optical properties and provides practitioners with actionable insights and best practices for using these methods.