Increased portability, versatility and ubiquity of electronics devices are a result of their progressive miniaturization, requiring current flow through narrow channels. Present-day devices operate close to the maximum current-carrying-capacity (that is, ampacity) of conductors (such as copper and gold), leading to decreased lifetime and performance, creating demand for new conductors with higher ampacity. Ampacity represents the maximum current-carrying capacity of the object that depends both on the structure and material. Here we report a carbon nanotube–copper composite exhibiting similar conductivity (2.3–4.7 × 105 S cm−1) as copper (5.8 × 105 S cm−1), but with a 100-times higher ampacity (6 × 108 A cm−2). Vacuum experiments demonstrate that carbon nanotubes suppress the primary failure pathways in copper as observed by the increased copper diffusion activation energy (~2.0 eV) in carbon nanotube–copper composite, explaining its higher ampacity. This is the only material with both high conductivity and high ampacity, making it uniquely suited for applications in microscale electronics and inverters.