Steelmaking is responsible for 7% of the global net emissions of carbon dioxide and heavily reducing emissions from currently dominating steelmaking processes is difficult and costly. Recently, new steelmaking processes based on the reduction of iron ore with hydrogen (H-2) produced via water electrolysis have been suggested. If the electricity input to such processes is fossil-free, near-zero carbon dioxide emissions steelmaking is achievable. However, the high electricity demand of electrolysis is a significant implementation barrier. A H-2 storage may alleviate this via allowing a larger share of H-2 to be produced at low electricity prices. However, accurately forecasting electricity market dynamics is challenging. This increases the risk of investment in a H-2 storage. Here we evaluate a novel methanol-based H-2 storage concept for H-2-based steelmaking that also allows for the coproduction of methanol. During electricity price peaks, the methanol can be reformed to produce H-2 for the steelmaking process. During prolonged periods of low electricity prices, excess methanol can be produced and sold off, thus improving the prospects of storage profitability. We use historical electricity prices and a process model to evaluate methanol and fossil-free steel co-production schemes. Methanol co-production is found to have the potential to improve the economics of H-2 supply to a fossil-free steelmaking process by up to an average of 0.40 (sic)/kg H-2 across considered scenarios, equivalent to a 25.0% reduction in H-2 production electricity costs.