A continuous rise in the global demand for palm oil has resulted in the large‐scale expansion of oil palm plantations and generated environmental controversy. Efforts to increase the sustainability of oil palm cultivation include the recycling of oil‐mill and pruning residues in the field, but this may increase soil CH4 (methane) emissions. This study reports the results of yearlong field‐based measurements of soil N20 (nitrous oxide) and CH4 emissions from commercial plantations in North Sumatra, Indonesia. One experiment investigated the effects of soil‐water saturation on N20 and CH4 emissions across inorganic fertilisers and organic amendments by simulating 25 mm rainfall per day for 21 days. Three additional experiments focused on emissions from a) inorganic fertiliser (urea), b) combination of enriched mulch with urea and c) organic amendments (empty fruit bunches, enriched mulch and pruned oil palm fronds) applied in different doses and spatial layouts (placed in inter‐row zones, piles, patches or bands) for a full year. The higher dose of urea led to a significantly higher N20 emissions with the emission factors ranging from 2.4‐2.7% in the long‐term experiment, which is considerably higher than the IPCC standard of 1%. Organic amendments were a significant source of both N20 and CH4 emissions, but, N20 emissions from organic amendments were 66‐86% lower than those from inorganic fertilisers. Organic amendments applied in piles emitted 63 and 71% more N20 and CH4 respectively than when spread out. With twice the dose of organic amendments, cumulative emissions were up to three times greater. The (simulated) rainwater experiment showed that the increase in precipitation led to a significant increase in N20 emissions significantly, suggesting that the time of fertilisation is a critical management option for reducing emissions. The results from this study could therefore help guide residue and nutrient management practices to reduce emissions while ensuring better nutrient recycling for sustainable oil palm production systems.