This study analyses the spatial distribution of hydrogen demand for industry feedstock, high-temperature process heat, heavy-duty goods transport, shipping and aviation in Switzerland and then cost-optimizes coupled electricity and hydrogen systems at a high spatial and temporal resolution in 2035 and 2050. Three scenarios of how hydrogen markets could develop are considered: Hydrogen economy, Hydrogen as a niche, and Midway. The results show that hydrogen in Switzerland can be fully provided from renewable electricity, best in regions with hydropower or wind power and near hydrogen demand sites. Hydrogen has only marginal potential though for re-conversion as electricity storage or for replacing natural gas in combustion plants. As hydrogen storage in compressed tanks is not cost-effective in Switzerland, intermediate storage in hydrogen transport trucks as well as hydrogen export to neighbouring countries with underground storage are favourable. Under conservative assumptions of hydrogen import costs, Switzerland could be a competitive hydrogen exporter.