Wearable sensors are widely used to gather psychophysiological data in the laboratory and real-world applications. However, the accuracy of these devices should be carefully assessed. The study focused on testing the accuracy of the Empatica 4 (E4) wristband for the detection of heart rate variability (HRV) and electrodermal activity (EDA) metrics in stress-inducing conditions and growing-risk driving scenarios. Fourteen healthy subjects were recruited for the experimental campaign, where HRV and EDA were recorded over six experimental conditions (Baseline, Video Clip, Scream, No-Risk Driving, Low-Risk Driving, and High-Risk Driving) and by means of two measurement systems: the E4 device and a gold standard system. The overall quality of the E4 data was investigated; agreement and reliability were assessed by performing a Bland–Altman analysis and by computing the Spearman’s correlation coefficient. HRV time-domain parameters reported high reliability levels in Baseline (r > 0.72), Video Clip (r > 0.71), and No-Risk Driving (r > 0.67), while HRV frequency domain parameters were sufficient in Baseline (r > 0.58), Video Clip (r > 0.59), No-Risk (r > 0.51), and Low-Risk Driving (r > 0.52). As for the EDA parameters, no correlation was found. Further studies could enhance the HRV and EDA quality through further optimizations of the acquisition protocol and improvement of the processing algorithms.