Solid state lighting is becoming a popular light source for color vision experiments. One of the advantages of light emitting diodes (LEDs) is the possibility to shape the target light spectrum according to the experimenter's needs. In this paper, we present a method for creating metameric lights with an LED-based spectrally tunable illuminator. The equipment we use consists of six Gamma Scientific RS-5B lamps, each containing nine different LEDs and a 1 m integrating sphere. We provide a method for describing the (almost) entire set of illuminant metamers. It will be shown that the main difficulty in describing this set arises as the result of the intensity dependent peak-wavelength shift, which is manifested by the majority of the LEDs used by the illuminators of this type. We define the normalized metamer set describing all illuminator spectra that colorimetrically match a given chromaticity. Finally, we describe a method for choosing the smoothest or least smooth metamer from the entire set.