Functionalisation of carbon nanotubes by carbene derivatives is attracting attention as a way of increasing their dispersibility, processability and also to control the electronic properties of carbon nanotubes. We have explored the functionalisation of a sample containing single- and double-walled carbon nanotubes with different diaryldiazomethane derivatives by using the high reactivity of the intermediate carbenes formed under actinic irradiation to insert to the carbon nanotube structure. Besides characterisation by bulk techniques (Raman, FTIR and TGA), we provide direct evidence on the location of the functional groups on the sidewalls of the carbon nanotubes by an electron microscopy study of a heavy-element tagged sample. The functionalised carbon nanotubes present higher dispersibilities than the purified samples and are prone to further derivatisation, with potential application in the areas of composite materials or molecular electronics.