I think Charles Stross does this pretty nicely, although his science part is not very hard science. So he's basically not predicting anything, his science fiction is more of the "ok I know this is not real but what if it were" variety.
The Laundry Files series is "what if Lovecraft was right and there's magic math that can summon the old gods", but then add to it that we do have a way to do tons of math stuff in the form of computers. So of course what happens? Well, there are spy agencies tasked with controlling this, because we can't get rid of computers, too important, but also, we can't let that magic math run wildly.
The Merchant Princes series is "what if there was a way to travel to an alternate dimension". So what happens? The dudes from the alternate dimension, who are the ones that discovered the secret, and come from a medieval-like world, use that to smuggle shit. They can go near the border, jump to the other side where the border doesn't exist (or at least doesn't exist right there) walk a couple of miles, and then jump back to our world. They of course build a massive criminal empire on our side. On the other side, they bring our advanced tech gadgets back and they are a hugely powerful merchant family. There's also all the implications for security. You can jump inside any building as long as you know exactly where it is on the other side. And the shit the US government gets up to when they discover this exists is pretty disturbing (especially when you consider that it makes sense given what was done in the name of the war on terror).
A note on this: the series is written under the Jack Campbell pseudonym. Took me a while to find. The first book is Dauntless