In face of the ongoing climate change, both reduction and offsetting of carbon emissions are critical. To this end, accurate, reliable emission data, and service-oriented architectures for processing the data are needed. Current carbon accounting practices, however, are often error-prone, costly, and time-consuming. Even in digital monitoring, reporting, and verification (MRV) systems, the employment of single, trusted verification bodies inhibits transparent, fine-granular, and verifiable accounting at product instance-level in high-throughput supply chains. We proposeVerifiable Carbon Accounting(VCA) as a novel accounting approach that leverages authenticity and zero-knowledge proofs in service-oriented architectures for creating non-disclosing emission reports that are peer-to-peer verifiable on blockchains. VCA builds upon and extends both conventional and digital MRV systems but ensures the confidentiality of business emission data and calculations while allowing for peer-to-peer transparency and verifiability. We introduce the concept and demonstrate VCA application for accounting product carbon footprints (PCFs) in supply chains. We present a proof-of-concept technical system design and implementation and discuss experimental findings, deriving both insights on VCA practicability and next steps. Overall, we show how VCA advances the state of the art in carbon accounting in and beyond supply chains, and how VCA can serve as the basis for next-generation, accurate carbon accounting.