George Church is probably one of the foremost experts in Neanderthal genetics. Such an expert is he, that he was the subject of multiple tabloid newspaper articles concerning the idea of seeking a surrogate "Neanderthal Mom."
If you'll remember a few years ago when Dolly the sheep was cloned, scientists used a sheep to implant the cloned DNA into and Dolly was brought to term. This is similar to the idea these tabloids say Church had. Church however denied this and added that the public needs more "scientific literacy" to discern fact from fiction. Church was merely theorizing on what would be necessary to bring a Neanderthal child into the world. Church is not looking for a willing female human to implant a potential embryo into, but he does appreciate the attention it has drawn to science. It would be interesting to see this kind of experiment, but I'm not sure the world is ready for the Neanderthal to return. There are a plethora of questions surrounding even the idea of cloning a Neanderthal: Would they be treated as beings or test subjects; how many would be created; what would be done with them after the experiment was over. The Neanderthal has been extinct for 30,000 years (though by looking at some people you'd never know they missed a beat). I would be first on line to see the first Neanderthal baby, considering how much theorizing I've done on the evolution of our species, but this simply should not happen. At least not yet. Things would go wrong, the Neanderthal would somehow be exploited. We as a species are not ready to deal with our old rivals. It would end badly.