Product matching, i.e., being able to infer the product being sold for a merchant-created offer, is crucial for any e-commerce marketplace, enabling product-based navigation, price comparisons, product reviews, etc. This problem proves a challenging task, mostly due to the extent of product catalog, data heterogeneity, missing product representants, and varying levels of data quality. Moreover, new products are being introduced every day, making it difficult to cast the problem as a classification task. In this work, we apply BERT-based models in a similarity learning setup to solve the product matching problem. We provide a thorough ablation study, showing the impact of architecture and training objective choices. Application of transformer-based architectures and proper sampling techniques significantly boosts performance for a range of e-commerce domains, allowing for production deployment.