Image processing with artificial intelligence has shown significant promise in various medical imaging applications. The present study aims to evaluate the performance of 16 different convolutional neural networks (CNNs) in predicting age and gender from panoramic radiographs in children and young adults. The networks tested included DarkNet-19, DarkNet-53, Inception-ResNet-v2, VGG-19, DenseNet-201, ResNet-50, GoogLeNet, VGG-16, SqueezeNet, ResNet-101, ResNet-18, ShuffleNet, MobileNet-v2, NasNet-Mobile, AlexNet, and Xception. These networks were trained on a dataset of 7336 radiographs from individuals aged between 5 and 21. Age and gender estimation accuracy and mean absolute age prediction errors were evaluated on 340 radiographs. Statistical analyses were conducted using Shapiro–Wilk, one-way ANOVA, and Tukey tests (p < 0.05). The gender prediction accuracy and the mean absolute age prediction error were, respectively, 87.94% and 0.582 for DarkNet-53, 86.18% and 0.427 for DarkNet-19, 84.71% and 0.703 for GoogLeNet, 81.76% and 0.756 for DenseNet-201, 81.76% and 1.115 for ResNet-18, 80.88% and 0.650 for VGG-19, 79.41% and 0.988 for SqueezeNet, 79.12% and 0.682 for Inception-Resnet-v2, 78.24% and 0.747 for ResNet-50, 77.35% and 1.047 for VGG-16, 76.47% and 1.109 for Xception, 75.88% and 0.977 for ResNet-101, 73.24% and 0.894 for ShuffleNet, 72.35% and 1.206 for AlexNet, 71.18% and 1.094 for NasNet-Mobile, and 62.94% and 1.327 for MobileNet-v2. No statistical difference in age prediction performance was found between DarkNet-19 and DarkNet-53, which demonstrated the most successful age estimation results. Despite these promising results, all tested CNNs performed below 90% accuracy and were not deemed suitable for clinical use. Future studies should continue with more-advanced networks and larger datasets.