Firstly do you need to quantify accurately the intangible benefits or could you just describe them in a qualitative terms. i.e. the business case is clearly made and justifiable based on tangible benefits alone.
If the case is less clear then consider why the benefits are considered intangible. Is it because they cant be measured or that the data to measure them does not exist or is not in the right format or granularity. If it is the later then consider implementing a process to make the intangible - tangible (resources and time allowing).
If it is the former then you need to find another way of quantifying the qualitative. I have used a number of methods in the past, usually a combination of collection, analysis and interpretation tools or methods.
these might include AHP, Statistical, scenario and/or comparative analysis, elimination and reduction processes etc. In my thesis available on RG, i have a chapter on the use of AHP and statistical analysis as well as multi criteria decision making which may be useful.