How do you up-rez 1080 footage? Can you?

In the olden days of the mid-2000s there were some fairly sophisticated software tools (Genuine Fractals) and clever techniques to undetectably increase the resolution of digital still photos... Is there anything similar in Resolve for video? I have some 1080 footage that I'd like to incorporate into a short 4K video. Or is Resolve so amazing that it will do a good job of up-rezzing when I export the footage to it’s final format?

There is nothing amazing at all in Resolve for this. It will do normal scaling.

There are open source tools for neural network based+other techniques scaling. There are some AE plugins which are quite often crazy slow and still not very good.

There is this:
http://www.mtifilm.com/cortex-enterprise-v4
with:
"MTI HQ and MTI-Samsung UpRes to 4k & Beyond. Resolution Independent Up or down resizing with industry leading algorithm, MTI HQ and MTI-Samsung. Bringing UHD quality to HD content."
but it will cost you good money. Have not seen results but it maybe good- specially Samsung algorithm as they work with universities to make something better than typical approach (for their TVs).

There is also something in Nucoda, but when I tried it long time ago it was not that great.
Most tools promise a lot, but end result is quite often not worth extra time over standard Lanczos3/Spline scaling.

This renderer https://forum.doom9.org/showthread.php?t=146228 has some crazy advanced GPU based scaling options, but not sure if you can use it for creating file (rather than just viewing it).

Or try OFX BORIS BCC UpRez ?

Thank you both. Great information.

There is also a crazy good upscaler for drawn footage. It's not usable for anything else, but if you ever want to scale up some old animation or something have a look:

https://github.com/nagadomi/waifu2x
Demo Website: http://waifu2x.udp.jp/

Or try OFX BORIS BCC UpRez ?

same answer here when working in Resolve,

but i try to avoid scaleing in Resolve and send the shots to something that offers lancos + filtering as the first option, like Nucoda or Baselight