For indexing the content of digitized historical texts, optical character recognition (OCR) errors are a hampering problem. To explore the effectivity of new strategies for OCR post-correction, this article focuses on methods of character-based machine translation, specifically neural machine translation and statistical machine translation. Using the ICDAR 2017 data set on OCR post-correction for English and French, we experiment with different strategies for error detection and error correction. We analyze how OCR post-correction with NMT can profit from using additional information and show that SMT and NMT can benefit from each other for these tasks. An ensemble of our models reached best performance in ICDAR’s 2017 error correction subtask and performed competitively in error detection. However, our experimental results also suggest that tuning supervised learning for OCR post-correction of texts from different sources, text types (periodicals and monographs), time periods and languages is a difficult task: the data on which the MT systems are trained have a large influence on which methods and features work best. Conclusive and generally applicable insights are hard to achieve.