No compensation. ATC restrictions are outside the airline's control.
Check your flightAir traffic control restrictions, ATC staff strikes, airspace closures, and flow management delays are extraordinary circumstances. The airline has no influence over them, so no compensation is payable when one genuinely causes your delay.
This is a real and frequent cause. European airspace runs close to capacity in summer, and a single ATC issue can cascade across a whole day of departures.
Two things are still worth doing. First, claim your duty of care, because meals and hotels are owed regardless of cause. Second, check the timing. If ATC problems occurred in the morning and your evening flight was delayed, the airline may be attributing a knock-on delay from its own late aircraft to an ATC event that had already cleared. That knock-on delay is the airline's responsibility, not ATC's.
Compensation is a flat amount set by distance, not by ticket price: €250 up to 1,500 km, €400 for longer flights inside the EU and for 1,500–3,500 km, and €600 beyond 3,500 km. The UK equivalents are £220, £350 and £520.
Distance is measured in a straight line from your original departure airport to your final destination, which on a connecting itinerary often lands you in a higher band than you would expect.
Duty of care is separate from compensation and does not depend on the cause. Once you are delayed two hours or more the airline owes you meals and drinks, two phone calls, and a hotel plus transfers if you are stuck overnight. This applies in bad weather, during ATC strikes, and in every other situation where no compensation is payable.
Airlines frequently provide none of this during major disruption. Buy your own, keep every receipt, and claim the cost back afterwards.
Work out what you are owed