Seaweeds are an extremely important marine resource in coastal systems globally, with substantial potential for human food, feed additives, methane reduction from ruminants and novel products. Increasing seaweed stocks, particularly via aquaculture including into the open ocean, has been widely promoted as a natural, safe and simple solution to climate change via the photosynthetic fixation of atmospheric carbon dioxide and the subsequent sequestration of carbon as living biomass or into sediments: seaweed carbon credits are being sold on the voluntary carbon market on this basis. However, the optimism and enthusiasm afforded by seaweed ‘afforestation’ for carbon dioxide removal (CDR) is not currently supported by underpinning science. Here we consider how a very complex solution for CDR has gained such popularity, then outline best scientific practices required to assess CDR by seaweeds using a Forensic Carbon Accounting framework, and also highlight other, more tractable, methods by which seaweeds might assist in climate mitigation.