We assess the capabilities of large language models on tasks involving Buddhist texts written in Sanskrit and Classical Tibetan—two typologically distinct, low-resource historical languages. To this end, we introduce DharmaBench, a benchmark suite comprising 13 classification and detection tasks grounded in Buddhist textual traditions: six in Sanskrit and seven in Tibetan, with four shared across both. The tasks are curated from scratch, tailored to the linguistic and cultural characteristics of each language. We evaluate a range of models, from proprietary systems like GPT-4o to smaller, domain-specific open-weight models, analyzing their performance across tasks and languages. All datasets and code are publicly released, under the CC-BY-4 License and the Apache-2.0 License respectively, to support research on historical language processing and the development of culturally inclusive NLP systems.