details in screenshots

[whatchitfoool]

Im looking for advice on manipulating the most detail out of screen shots. Im talking items in the background, text on objects, physical properties, ect. 
Currently, im using virtualDub to extract frames in TARGA. I then take it into photopshop and save it as a TIF, and work with it from there.

Id like to be able to enlarge parts of the frame (or the whole frame) for peeping digitally, or maybe even for a large format print.  Ive tried some SR but havn't had great results. I've read on SR and understand the theory,  but could use any input on practical applications and software to use.

Anyone have any input on the matter?

[spoRv]

The fact is, there is no perfect upscaling solution for every source; there will be always some compromise between details, ringing etc. so, the simple answer to the question "which is the best upscaling method" is "it depends!"

My experience with the SR is that it works quite well when the source is low resolution and you have to zoom 2x, max 4x; NNEDI3 does a great job, too; remember that for intermediate zoom, best way is to upscale with SR or NNEDI3 using the power of 2 (2x, 4x, 8x etc) and then downscale using another algorhythm.

You can always combine both in several ways, along with other methods, and test which do you like most; you can, for example, SR upscale + lanczos downscale, NEEDI3 upscale + spline downscale, combine both with various mix percentage... there is a lot of hard work, but fun at the same time - well, if you are a nerd, at least!

Last thing: the most promising way is to use deep learning - there is a google service available IIRC.