Membranous nephropathy (MN) is among the most common glomerular diseases that cause nephrotic syndrome in adults. To aid pathologists on performing the MN classification task, we proposed here a pipeline consisted of two steps. Firstly, we assessed four deep-learning-based architectures, namely, ResNet-18, MobileNet, DenseNet, and Wide-ResNet. To achieve more reliable predictions, we adopted and extensively evaluated a Monte-Carlo dropout approach for uncertainty estimation. Using a 10-fold cross-validation setup, all models achieved average F1-scores above 92%, where the highest average value of 93.2% was obtained by using Wide-ResNet. Regarding uncertainty estimation with Wide-ResNet, high uncertainty scores were more associated with erroneous predictions, demonstrating that our approach can assist pathologists in interpreting the predictions with high reliability. We show that uncertainty-based thresholds for decision referral can greatly improve classification performance, increas-ing the accuracy up to 96%. Finally, we investigated how the uncertainty scores relate to complexity scores defined by pathologists