Colour produced by wavelength-dependent light scattering is a key component of visual communication in nature and acts particularly strongly in visual signalling by structurally-coloured animals during courtship. Two miniature peacock spiders (Maratus robinsoni and M. chrysomelas) court females using tiny structured scales (~ 40 × 10 μm2) that reflect the full visual spectrum. Using TEM and optical modelling, we show that the spiders' scales have 2D nanogratings on microscale 3D convex surfaces with at least twice the resolving power of a conventional 2D diffraction grating of the same period. Whereas the long optical path lengths required for light-dispersive components to resolve individual wavelengths constrain current spectrometers to bulky sizes, our nano-3D printed prototypes demonstrate that the design principle of the peacock spiders' scales could inspire novel, miniature light-dispersive components.