SHETLAND, Scotland—On the windswept hills that line the west coast of the Shetland Islands, roaming sheep bear lonely witness to a surprising industrial comeback.

A gray, metal-and-concrete skeleton slowly emerging from the peat bogs makes up the last leg of Laggan-Tormore, Total SA’s FP.FR -1.75% £3.3 billion ($5 billion) project to extract natural gas from the North Sea’s wild western edge. For more than 25 years since its discovery, the field has lain trapped beneath a bed of hard rock and deep, stormy waters. But the French oil company says that by the summer of next year, the gas finally will be liberated, meeting 5% of the U.K.’s needs.

It is a story that has been repeated elsewhere, confounding expectations of decline in the North Sea. Areas that 10 years ago were thought to be thoroughly exploited, or too technically challenging, now are yielding major new developments

“Technology and science showed there is oil where people thought there wouldn’t be oil any more,” says Manoucherh Takin, from the London-based Center for Global Energy Studies.

U.K. North Sea oil and gas production has dropped by more than half since its peak of around 4.6 million barrels a day in 1999 as aging fields have become depleted. Norway’s similar-size peak came five years later, but production has dropped almost 15% since then.

But now, new technology, assisted by higher oil prices and modest tax incentives, is forecast to reverse that decline.

This will bring significant economic benefits for both countries. The U.K. oil industry employs around 440,000 people and last year contributed £11.5 billion to flagging government coffers—more than any other sector. Oil and gas accounts for half of Norway’s exports and 20% of its gross domestic product.

Interest in the North Sea among international energy companies has been so great that support services are in danger of maxing out.

West of the U.K.’s Shetland Islands, where the North Sea merges into the Atlantic Ocean, lies the distant Laggan-Tormore discovery. “There are mighty storms, the subsea water is very cold,” says Jean-Pierre Minster, the head of research and development for Total.

The extreme environment meant the standard way of tapping offshore oil since the 1960s, a steel platform on the surface, would have been too risky and costly, says Patrice de Viviès, the company’s vice president for Northern Europe.

After years of research, technology that didn’t exist when the field was discovered in 1986 became the key to unlock its potential, he says.

Total reinforced its drill bits to pierce the hard sedimentary rock above the reservoir, Mr. Minster says. It avoided the stormy surface by locating extraction equipment on the sea bed and will operate it remotely from shore. To overcome the extreme subsea cold, the company found new insulating materials to sheath pipes that carry gas from the wells to the shore.

New technology has enabled other nearby developments.

Advanced seismic sensors on the sea floor, providing a clearer image of geological structures than previously possible, will enable Chevron Corp. CVX +1.22% and its partners to drill more-efficiently targeted wells to develop the $6 billion to $8 billion Rosebank project, the U.S.-based company says. The project could eventually yield as much as 240 million barrels of oil equivalent, making it one of the largest new U.K. prospects.

BP BP.LN -1.40% PLC says new ways of gathering and processing seismic data are helping the British company and its partners move ahead with a third phase of the $9 billion Clair field development, originally discovered in 1977.

Within five years, fields west of Shetland are expected to produce 17% of the U.K.’s oil and gas, says Total’s Mr. de Vivies. That will help the country’s production rebound back above two million barrels of oil equivalent a day by 2017, compared with 1.55 million barrels last year, according to Oil & Gas U.K., a trade group.

The second area driving the North Sea revival is around 200 miles southeast of Laggan-Tormore, in Norwegian waters, where Sweden’s Lundin Petroleum AB LUPE.SK -0.39% has been digging through major oil companies’ leftovers.

“The consensus at the end of the ’90s was that the fall [in discoveries] on the Norwegian shelf was due to a lack of resources,” says Hans Christen Rønnevik, Lundin’s exploration manager. “That was a view we didn’t subscribe to.”

“We are hard-core geologists and geophysicists who look at data and interpret them in new ways,” he says. By looking through old seismic surveys with a modern eye, Lundin guessed that there was a big undiscovered field in the Utsira High, a geological structure that is one of the most heavily-drilled areas in Norway, he said.

The company gathered three-dimensional seismic data using technology that produces higher resolution images than old techniques, Mr. Rønnevik says.

Finally, in September 2010, Lundin drilled what turned out to be the largest oil discovery in Norway in about three decades, now called Johan Sverdrup and shared with Norwegian state oil company Statoil STL.OS -0.22% ASA. The field contains an estimated 1.7 billion to 3.3 billion barrels of recoverable oil, equivalent to up to six times Norway’s current annual crude output.

That discovery has inspired others. Statoil this month said it had found between 40 million and 150 million additional barrels of oil and gas near the Gullfaks license in the northern North Sea, a field which started production back in 1986.

“We’re also tending to look at the edges, underneath and between reservoirs that we’ve already found,” says Trevor Garlick, regional president for BP North Sea.

Such discoveries could mean that Norway “will continue to discover as much as one billion barrels every year for the next 20 years,” says Jarand Rystad, chief executive of Oslo-based consulting firm Rystad Energy AS.

The Norwegian Petroleum Directorate says it expects the country’s total oil and gas production to bottom out at 3.7 million barrels of oil equivalent a day this year and rebound to 3.8 million barrels by 2017.

There is a danger that the North Sea could fall victim to its own success.

As activity increases, the supply chain is being stretched, says Ross Cassidy, lead Norway analyst at U.K.-based consulting firm Wood Mackenzie. The availability of drilling rigs has become a problem, particularly in Norway, where drilling for around five of the 50 wells expected to be sunk this year have been delayed because of rig shortages, he said.

“That’s the No. 1 challenge,” to the revival of the region, Mr. Cassidy says.