Using ordinary digital cameras as relatively cheap measurement devices for estimating spectral color properties has become an interesting alternative to making pointwise high precision spectral measurements with special equipments like photospectrometers. The results obtained with these methods cannot compete with the quality of the traditional high resolution devices but they are very attractive since the equipment is relatively cheap and instant measurements are obtained for millions of measurement points.In this paper we investigate the problem of estimating reflectance spectra from measurements taken with ordinary digital RGB cameras. We study the effects of using multiple illuminations and treat the estimation of the reflectance spectra as a regression or a statistical inversion problem. We use both, linear- and non-linear estimation methods where we focus on using reproducing kernels to avoid explicit formulation of non-linearities. We also include non-linear conditions based on the properties of the reflection spectra. Munsell Matte color and Pantone are used as data sets to support the proposed methods. The experiments show that the proposed methods improve the estimation results when compared to standard linear methods.