The EU climate chief will head to the US next week to defend the bloc's carbon charge on flights to the EU.
The law, which officially took effect on Jan. 1, has a long lead time, so none of the airlines faces a bill until next year after their emissions have been calculated.
Before then, a series of smaller deadlines will elapse for submitting data under the EU's complicated Emissions Trading Scheme (ETS) to cap climate-warming greenhouse gases from power generators, heavy industry and now airlines.
Governments, airlines and planemakers have warned it could lead to chaos in the skies and a trade war.
India said this week it would ignore the next one on March 31, following on from noisy protests from China, which has linked suspension of $14 billion of jet orders from European planemaker Airbus to its fury with the EU.
Airbus's arch-rival, U.S.-based plane-maker Boeing, has for once found common cause with Airbus in its dislike of the EU scheme.
In a meeting last month in Moscow of the so-called "coalition of the unwilling", countries opposed to the EU law agreed on retaliatory steps, though they did not agree on enforcing them.
EU Climate Commissioner Connie Hedegaard has said time and again the only reason for the EU to alter course would be if the United Nations' International Civil Aviation Organization (ICAO) could come up with a global plan to tackle rising carbon emissions from the sector.
"It's not that you can threaten us to change the law," she said last month.
"It's one thing that they do not like what Europe is doing. What can they agree to in ICAO?"
Next week Hedegaard will be in Washington to discuss transatlantic climate issues with U.S. administration officials and members of Congress and to receive a Women and the Green Economy Leadership Award.
On this issue, the United States has been less appreciative of her leadership.
It has sent her letters of complaint about the ETS and threatened, but stopped short of agreeing, blocking legislation in Congress.
So far, U.S. airlines are complying grudgingly.
The penalties for breach of the EU law start at 100 euros for every tonne of carbon airlines fail to pay for, while the cost of compliance is estimated at about 2 euros per passenger for a flight from Shanghai to Frankfurt.
Persistent offenders could find their flights banned.
That might trigger international air chaos if other countries retaliate, as they say they might.
Opponents say it is about national sovereignty, not cost.
The EU adopted its law in 2009 after well over a decade of inaction by the ICAO to address rising emissions, and in December last year, Europe's highest court found the EU's law was valid.
Before agreeing it, the EU's executive arm consulted stakeholders, including airlines.
At the time the airlines said they would prefer a market-based ETS to a straightforward tax, but they have since said it depended on how it was implemented.
While support from governments beyond the bloc has been lacking, within the EU all 27 member states have held firm publicly, with ministers and the European Parliament both reiterating their backing this month.
All sides in the row say they are looking to the ICAO to redouble efforts to find a solution on which everyone can agree.
But no one expects any kind of decision before the end of the year, conveniently after the election in the United States, where climate policy has become a battleground between President Barack Obama and his opponents.
Even then, EU sources, analysts and aviation lawyers say they are not hopeful of a global agreement, given the ICAO's track record so far.
Its members include the same governments that issued trade war threats and held breakaway meetings to draw up a battle plan.
"Even if ICAO could manufacture some sort of draft treaty, that doesn't mean anyone is going to be willing to sign and ratify it," said Gabriel Sanchez, adjunct professor of law at the International Aviation Law Institute at Chicago's DePaul University.
"The EU might still find an ICAO-brokered treaty to be insufficient to address the emissions issue and therefore still keep its ETS in place."
The question remains whether Europe can hold its nerve or agree to a classic European fudge.
It could, for instance, waive emissions charges for the non-European section of flights in and out of EU airports, to alleviate sovereignty concerns.
Hedegaard says she is determined to build on success at U.N. climate change talks in Durban last year.
Progress there was incremental rather than revolutionary, but Hedegaard's experience of dealing with 27 member states every day helped her play a lead role in getting nearly 200 nations to keep the Kyoto climate-change process alive.
"As we did in Durban, the EU will continue to set the pace and fight for more ambition here and abroad. We will continue working to get all our partners on board for the ambitious action our planet demands," she wrote in an opinion piece.
For all the difficulties over airlines, the Commission says it is pressing ahead with plans to tackle shipping emissions and is expected to announce proposals later in the year.
Most observers, however, predict some kind of levy rather than an attempt to draw another global sector into the complicated and controversial ETS.