We demonstrate broadband, near perfect absorption with a conformal coating of a multi-walled carbon nanotube (CNT) forest on an arbitrarily shaped surface. The complex refractive index of such a CNT forest is retrieved from the measured transmission and reflection spectra using Kramers-Kronig constrained variational analysis, which gives a typical value of neff = 1.04 + 0.01i at visible wavelengths. Therefore, when used as a conformal coating on an object, a thick layer of the CNT forest can provide an excellent impedance match to air and near perfect absorption, preventing any detectable light reflection and scattering from the object.