But flights remained grounded in large parts of the continent as authorities across Europe said there was no end in sight to the plume spewing out of a volcano in Iceland that they insist is dangerous to planes.
Millions of passengers have had plans foiled or delayed because of a ban on air travel that has gradually expanded over large swaths of Europe since Thursday.
The aviation industry, already reeling from a punishing economic period, is facing at least $200 million in losses every day, according to the International Air Transport Association.
With airspace closed (or partially closed) in 24 countries, a series of European research flights were the first sign that attitudes - if not the ash cloud itself - might be shifting.
German and Dutch flights were sent up to determine just how dangerous to jet engines the volcanic ash cloud is, reports CBS News correspondent Mark Phillips.
The planes landed safely, and the Dutch airline KLM said it found no damage, but the effect on the engines is still being evaluated.
There is no relief meanwhile for the tens of thousands of stranded passengers -- and no dramatic change predicted in the weather pattern that has kept the ash cloud where it is.
The airline says it now plans to return seven airplanes without passengers to Amsterdam from Duesseldorf Sunday.
"We hope to receive permission as soon as possible after that to start up our operation and to transport our passengers to their destinations," said Chief Executive Peter Hartman, who was aboard Saturday's flight.
Kyla Evans, spokeswoman for the European air traffic control agency Eurocontrol, said it was up to national aviation authorities to decide whether to open up their airspace. The agency's role was to coordinate traffic once it was allowed to resume.
Scientists say that because the volcano is situated below a glacial ice cap, magma is being cooled quickly, causing explosions and plumes of grit that can be catastrophic to plane engines, depending on prevailing winds.
In 1989, a KLM Boeing 747 that flew through a volcanic ash cloud above Alaska temporarily lost all four motors. The motors restarted at a lower altitude and the plane eventually landed safely.
In Saturday's test flight, a KLM Boeing 737, flew up to 41,000 feet, the maximum altitude at which the aircraft is certified to fly.
"We observed no irregularities either during the flight or during the initial inspection on the ground," Hartman said in a statement.
Also Saturday, Germany's Lufthansa flew 10 empty long-haul planes to Frankfurt from Munich at low altitude under so-called visual flight rules, in which pilots don't have to rely on their instruments.
The German restrictions allow such flights, so long as no passengers are on board, and German air traffic control said Air Berlin and Condor had carried out similar flights.
The Lufthansa planes flew at various levels between 3,000 and 8,000 meters, spokesman Wolfgang Weber said.
He stressed that the flights weren't tests, and were merely intended to get the planes in the right place at the Frankfurt hub for when restrictions are lifted.
"We simply checked every single aircraft very carefully after the landing in Frankfurt to see whether there was any damage that could have been caused by volcanic ash," Weber said. "Not the slightest scratch was found on any of the 10 planes."
He said Lufthansa didn't plan any more such transfer flights on Sunday.
The Swiss looked the other direction - above the ash cloud. The Swiss Federal Office of Civil Aviation began allowing flights Saturday above Swiss air space as long as the aircraft were at least at 36,000 feet. It also allowed flights at lower altitudes under visual flight rules, aimed at small, private aircraft.
Germany extended closure of its airports through 1800GMT Sunday and Britain until 0000 GMT, while the Dutch Transport Ministry said national airspace will remain closed to passenger traffic until at least 1200GMT Sunday, adding it is allowing further test flights.
"The goal of these test flights is to make measurements in Dutch airspace about the possible consequences of the ash on the airplane parts, the ministry said in a statement.
Airspace remained closed in Denmark, Finland and most parts of Sweden on Sunday. In Norway, authorities lifted air travel restrictions in the central part of the country, but kept airspace closed in other parts of the country, including the capital, Oslo.
Several world leaders, including President Barack Obama, had to abandon plans to attend the state funeral for Polish President Lech Kaczynski because of ash-related disruptions. Some low-level flights were being allowed in southern Poland, which is how the Polish Air Force was able to ferry the coffins of Kaczynski and his wife from Warsaw to Krakow aboard a prop-powered military cargo plane early Sunday morning.
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Southern Iceland's Eyjafjallajokull volcano began erupting for the second time in a month on Wednesday, sending ash several miles into the air. Winds have pushed the plume south and east across Britain, Ireland, Scandinavia and into the heart of Europe.
(Left: Wearing a mask against the smoke, Icelandic dairy farmer Berglind Hilmarsdottir from Nupur looks for cattle lost in the ash clouds Saturday, April 17, 2010.)
Around the world, anxious passengers have told stories of missed weddings, business deals and holidays because of the ominous plume. Stranded passengers reported the delays were causing financial hardships. Some had to check out of hotels and sleep in airports.
German Chancellor Angela Merkel was heading homeward Sunday in an armored car after spending the night in northern Italy - continuing a long and circuitous return from the United States.
Merkel was diverted to Portugal and continued to Rome on Saturday. The chancellor's delegation then took to Italy's highways in a convoy of an armored car and buses.
In Iceland, torrents of water have carried away chunks of ice the size of small houses. More floods from melting waters are expected as long as the volcano keeps erupting - and in 1821, the same volcano managed to erupt for more than a year.