The Tenerife Microwave Spectrometer (TMS) is a ground-based radio-spectrometer that will take absolute measurements of the sky between 10-20 GHz. To ensure the sensitivity and immunity to systematic errors of these measurements, TMS includes an internal calibration system optimised for the TMS band, and cooled down to 4 K. It consists of an Aluminium core, composed of a baseplate and a bed of pyramidal elements coated with an absorber material and a metallic shield. The absorber coating is made of a commercial resin ECCOSORB CR/MF 117. To achieve the high stability (+/- 1 mK/h), temperature homogeneity (thermal gradients {AT <= 25 mK), and emissivity (e>= 0.999) requirements of the reference unit, careful consideration has been given to the RF and thermal properties of the materials, as well as their geometry. In summary, this paper presents a comprehensive account of the design, characterisation, and test results of the TMS reference system.