Ask Chris Rapley, the ebullient physicist and director of the Science Museum in London, why he seems more sanguine about our prospects of taming climate change than many of his peers, and he'll tell you about the day he first toured the museum's library and archives. Surrounded by the thousands of designs and patent applications that traced the great Victorian lurch into modernity, he was struck by the power of human ingenuity. "It seemed clear that if we could somehow focus all that creativity and energy on clean energy then we'll be OK."

Anyone watching an hour or two of the "hearings" in Manchester last weekend on which this report was based could not fail to have been similarly cheered. The idea behind them was simple: we hear endlessly about the havoc unabated climate change will wreak, about long-term emissions targets and diplomatic wrangling over who will commit to them. But the countless ingenious ideas for tackling the problem emanating from universities, thinktanks, front rooms and sheds across the planet get rather less attention. So the Guardian teamed up with the Manchester International Festival to mount a search for the best of them.

Why Manchester? As the world's first great industrial city, it was arguably the birthplace of man-made warming. So just as Robert Angus Smith pioneered our understanding of atmospheric pollution here in the 1840s, experts and thinkers from around the world would gather in the city to grapple with the longer term legacy of its once mighty mills and factories.

To underscore the project's connection to the city's carbon hungry past, the hearings were held in Manchester Town Hall, Alfred Waterhouse's neo-gothic cathedral to manufacturing and mercantilism. Above the scientists, entrepreneurs and inconoclasts presenting their ideas, the great vaulted ceiling documented the countries and cities to which the city once dispatched its wares; outside the mosaic floors were decorated with the bees that embodied its 19th century self-image as a hive of industry.

The hearings themselves were perhaps best described as a cross between a judicial inquiry and an episode of the British TV show Dragons' Den. Chaired by Lord Bingham – formerly Britain's most senior judge – a panel of experts heard half hour pitches from advocates for each of 20 ideas shortlisted following a global appeal for innovative solutions to climate change. The panel, in consultation with the eminent climate scientist John Schellnhuber, picked the 10 most promising ideas – somewhat reluctantly since our experts felt all of the proposals aired in Manchester were worthy of more consideration. Now it's over to you: you can watch short video presentations of each of the ideas featured in this supplement on our website and vote for the ones you think will be most effective. Better still you might help to implement them by offering support or capital.

The ideas heard in Manchester ranged from the wackier edges of science fiction to well-advanced products poised to roll off production lines. From the wilder shores came Professor Stephen Salter, an Edinburgh University engineer with a plan to increase the whiteness of clouds using a fleet of remote-control sailing ships spraying a fine mist of seawater into the air. But anyone tempted to dismiss his plan as the product of a crank who has spent too much time in the shed would do well to note that Salter was the man behind the Edinburgh Duck, a pioneering 1970s design for harnessing wave energy.

Another variation on the marine theme came from former management consultant Tim Kruger who proposed tipping large amounts of lime into the ocean. This, he claimed, would increase the sea's ability to absorb carbon dioxide from the atmosphere as well as reduce the dangerous acidity which has also been a byproduct of decades of emissions. His compelling presentation was only slightly undermined by his own admission that such a plan would currently be illegal.

Mark Capron, a former naval engineer from California, was also frustrated by prosaic legal considerations. His idea involves farming algae out at sea and then digesting it in thousands of "giant stomachs" under the surface. The algae would absorb carbon dioxide and produce methane which could be used to produce energy. The trouble is that he fears building a prototype in his garage would breach local safety regulations.

Among the more developed ideas presented, Peter Scott made the case for simple, super-efficient cooking stoves. Burning wood (and other biomass) for cooking, largely in the developing world, was responsible for 10-20% of global emissions he told the panel. His stoves could cut the annual CO2 emissions of a household by 1-3 tonnes. The only downside, he noted ruefully, was that a local manufacturer in Malawi had been so successful that he had splashed out on a fleet of SUVs. "I haven't worked out the CO2 implications of that yet."

Another idea tantalisingly close to crossing the threshold from brainwave to reality was proposed by entrepeneur Mike Mason. He described dishwasher sized "ceramic fuel cells" which could produce enough electricity to power a home as well as hot water. Because they were vastly more efficient than the power stations which produce electricity for the grid, and also obviated the need for hugely wasteful transmission of power along along hundreds of miles of cable, they could achieve massive carbon savings. And the first domestic models would go on sale next year with a price tag of around £3,000.

Many green activists are intensely sceptical about the search for technological "fixes", particularly those that aim soley to mitigate the effects of warming. They warn that trying to invent our way out of trouble is a way of avoiding the changes to our way of life that are really required. But by no means all the advocates presenting in Manchester placed their faith in technology.

One of the most quietly inspiring presentations came from Rosemary Randall, a Cambridge psychotherapist who had been puzzled by the ability of people at the same time to acknowledge the threat of climate change and in no way change their high carbon lifestyle. Randall designed a series of "carbon conversations" in which she encourages people to explore their attitude to consumption, identity and status. People who have been on her course of six meetings typically reduce their emissions by a tonne immediately and then plan to cut in half within two to five years. Andrew Simms of the New Economics Foundation offered an even simpler prescription: consume less. It might even make us happier too.

Some of the ideas presented were so lateral that even our panel of seasoned experts looked wide-eyed at times. An engaging Australian accountant and farmer called Tony Lovell showed photographs of arid, dust-blown landscapes alongside images of lush vegetation. The difference? The farmer on the green side had been forcing his cattle to mimic the great migratory wildebeest herds of the Serengeti.

If some of the schemes outlined in Manchester would once have seemed too radical to attract serious attention from governments and money men, the presence of climate secretary Ed Miliband at the event suggested that policymakers now recognise that they must cast the net for solutions wider than in the past. Here we lay out the best ideas that our net brought in. Now, Mr Miliband, what will you do with them?

• Ian Katz is deputy editor of the Guardian responsible for environment coverage.