Methodology is probably not a strong point for international courts or international law in general.
In “Determining Customary International Law: The ICJ’s Methodology between Induction, Deduction and Assertion”, Stefan Talmon argues that: to determine the rules of customary international law, the ICJ does not use one single methodology but, instead, uses a mixture of induction, deduction and assertion. Interestingly, regardless what it may say on the subject, the Court in a majority of cases has not examined the practice and opinio juris of states. It has simply asserted the rules that it applies.
The abstract partly reads:
The article aims to refocus attention on the methodology used by the Court when determining the rules of customary international law that it applies, and it highlights the role played by methodology in the development of customary international law. It starts by defining the terms ‘induction’ and ‘deduction’ and examining their use by the Court. It then explores the situations in which the Court uses inductive and deductive reasoning, the different forms and functions of deduction and the relationship between the two methods. The article challenges the various theories distinguishing between inductive and deductive custom and demonstrates that the main method employed by the Court is neither induction nor deduction but, rather, assertion.
Text is available here.