Disclaimer: This is for most ;-) nvidia cards , i don't know if AMD cards have a similar function. Please add the how if you know it for AMD cards. [edit for correction of supported cards] With the current Nvidia cards there is an option called DSR (dynamic Sample Resolution), and is primary there for highres (upto 4K) rendering in gameplay. This high rendering will be down sampled to HD (1920-1080 res, or lower). The end image could/should be better then native HD, this is up to debate however because of the performance penalty you will suffer. But this function can also be used to take screenshots in 4K on a standard monitor or TV. This does not work with steam snapshot or in game photo taking. If you install the latest BETA of nvidia experience you get the new function SHARE, with that function you get also the option to take screenshots of the DSR resolution, thus up to 4K. The key for this is [ALT]-[F1] or other if you have custom keys. So if you drive in HD for performance in RR and set before a replay the resolution to 4K you can capture screenshots from your drive in 4K. See next example of resolution difference.
Just as addition for the AMD-Users: AMD has something very similar called VSR and is available on the following cards: AMD Radeon™ R9 Fury X GPU, AMD Radeon™ R9 300 Series, AMD Radeon™ R7 300 Series, AMD Radeon™ R7 260 and above GPUs, AMD Radeon™ HD 7900 Series, AMD Radeon™ HD 7800 Series, AMD Radeon™ HD 7790, and AMD A-Series APUs (A6 7400K and higher) I'm using it for month now with R3E and on my system it runs very well (specs below)
I never got it to work on my GTX770, maybe because they where in SLI. It was always grayed out. Thanks for this update.
Supported GPUs here: http://www.geforce.co.uk/hardware/technology/dsr/supported-gpus Seems it runs on more than just 700/900 series cards too.