When one puts in a claim for compensation under EU 261/2004 and the airline refuses to pay out (e.g. stating exceptional circumstances) what recourse does the traveller have? Is there a higher authority to take the claim to (like a tribunal or the like?)
Note the following text on the bottom of the 'Instructions' part of the complaint form however:
Please note that the competent authorities of Member States cannot in general take binding decisions on airlines in respect of individual complaints. If you are still not satisfied with the airline's response, even following the answer from the competent authority, you will have to pursue the matter in Court or through alternative dispute resolution.
Ultimately, your final recourse is through a relevant court or dispute tribunal process, which will depend on the countries and airlines involved. That doesn't really answer your question, but there are 28 EU countries plus associated other countries which enforce EU261, so a full list of the processes is out of the scope of this site - the Law StackExchange may help however.