Drone detection and localization (DDL) aims to identify and track aerial targets using sensors. This is crucial for several potential applications, such as surveillance, security, and safety-critical monitoring. Recent advances in uncertainty-aware deep learning have made reliable DDL increasingly viable. However, achieving both accurate predictions and trustworthy uncertainty estimates remains challenging under low signal-to-noise ratios (SNRs) and when distinguishing valid targets from noise-only failure cases. In this paper, we introduce two complementary uncertainty-aware frameworks for acoustic DDL based on conformal prediction and evidential learning, which provide distribution-free coverage guarantees and model-based uncertainty decomposition, respectively. We further compare their localization performance against a heteroscedastic regression baseline. Our results demonstrate that while conformal prediction reliably guarantees statistical coverage, evidential learning excels in correlating uncertainty with prediction error. However, analysis of noise-only inputs reveals that distinguishing valid targets from failure cases remains a critical challenge, as models tend to retain high confidence even on out-of-distribution data. These findings highlight the necessity of combining uncertainty methods to build robust DDL systems.