Hmm, I´m not having a paper in mind but I´d say that one way to do that is via turbidity measurements e.g. at 340 or 600 nm: You simply prepare solutions with increasing amounts of your substance and once the solubility limit is reached the turbidity should go up. Another approach is to measure the absorption directly - this however requires that the substance has an absorbance. Here you can also prepare some solutions that are saturated and others that are not. Measure the absorbance of the non-saturated solutions and spin down the saturated ones and then measure the absorbance in the saturated solutions. Depending on the extent of absorbance you may have to dilute samples. Take the measured absorbances and then put linear fits through the absorbances for the saturated solutions and for the non-saturated solutions as well. The intersection point of both lines is your solubility limit.
You may get inspired by this paper: http://www.ncbi.nlm.nih.gov/pubmed/7548045
But be aware, there are far better methods to determine a solubility limit than UV/Vis spectroscopy. Turbidity/Light scattering can be measured in 90° angle in a fluorescence spectrometer and the solubility of e.g. amino acids has been determined via oscillation densitometry over decades using the procedure with the saturated/non-saturated solutions i described above.
There is an instrument called a nephelometer (e.g. Nephelostar by BMG Labtech) that is useful for measuring compound solubility. It measures the light that is scattered to the sides by a turbid solution. It uses 96-well plates, so it can measure lots of samples, and it is very fast. We typically prepare a set of 2-fold serial dilutions of the compound in the desired buffer. The solubility limit is the highest concentration that has the same signal as the buffer alone.