Neonates undergoing surgery for congenital heart disease (CHD) are at high risk for brain function impairment. Reliable early predictors of postoperative neurological complications are lacking. We examined a retrospective cohort of 55 surgically treated CHD neonates systematically monitored by concomitant conventional electroencephalography (cEEG) and amplitude-integrated EEG (aEEG). Neonates underwent cEEG/aEEG at three time points: T0 (preoperative, duration: 90–120 min); T1 (24–48 h after cardiac surgery, duration: ≥11 h); and T2 (7–10 days post-surgery, duration: 90–120 min). For each patient, aEEG background activity was evaluated and scored, and clinical and surgical data were retrieved to establish short-term post-surgical outcomes. Patients with normal T0 monitoring had significantly higher aEEG bandwidths in T1. A lower Aristotle basic score was associated with an improvement in aEEG at T1. Inversely, a narrower aEEG bandwidth in T1 was associated with post-surgical neurological deterioration. The aEEG bandwidth accurately predicted short-term neurological outcome; in particular, a minimal aEEG amplitude above 17.5 µV excluded poor neurological outcome with a negative predictive value of 81.48%. Our results demonstrated that aEEG bandwidth and trend dynamics may be associated with surgical complexity and neurological outcomes. aEEG background trend monitoring may provide relevant prognostic information on neurological outcomes in surgically treated CHD neonates.