The loss of huge areas of peat swamp forest in Southeast Asia and the resulting negative environmental effects, both local and global, have led to an increasing interest in peat restoration in the region. Satellite remote sensing offers the potential to provide up‐to‐date information on peat swamp forest loss across large areas, and support spatial explicit conservation and restoration planning. Fusion of optical and radar remote sensing data may be particularly valuable in this context, as most peat swamp forests are in areas with high cloud cover, which limits the use of optical data. Radar data can ‘see through’ cloud, but experience so far has shown that it doesn't discriminate well between certain types of land cover. Various approaches to fusion exist, but there is little information on how they compare. To assess this untapped potential, we compare three different classification methods with Sentinel‐1 and Sentinel‐2 images to map the remnant distribution of peat swamp forest in the area surrounding Sungai Buluh Protection Forest, Sumatra, Indonesia. Results show that data fusion increases overall accuracy in one of the three methods, compared to the use of optical data only. When data fusion was used with the pixel‐based classification using the original pixel values, overall accuracy increased by a small, but statistically significant amount. Data fusion was not beneficial in the case of object‐based classification or pixel‐based classification using principal components. This indicates optical data are still the main source of information for land cover mapping in the region. Based on our findings, we provide methodological recommendations to help those involved in peatland restoration capitalize on the potential of big data.