I am a newcomer to the field/issue, but I have a few leads:
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the 3x LCD filter from Handy (Mednafen-Lynx probably includes this), is said to be the closest thing to the real thing Handy (in itself) has to offer;
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concerning shaders, the two talked about above are probably these ones: https://github.com/hizzlekizzle/quark-shaders/tree/master/LCD-cgwg.shader https://github.com/HarlequinVG/shaders/tree/master/lcd_shader
I have absolutely no idea about what those consoles are supposed to look like.
hunterk has done some screen comparisons between these two shaders: http://filthypants.blogspot.ca/2013/04/multipass-shaders-ntsc-motion-blur-and.html (see the “Harlequin’s LCD Shader” section);
If anyone has an idea to what is closest to the original both for the Lynx (1989) and the Game Boy Advance (2001), feel free to post opinions about shaders! will help us all