How do I play N64 virtual console games in widescreen on Wii U?

Try changing your tv settings under the screen mode, you should get a larger image that stretches it slightly, now go into your options on DK64 and change it to widescreen and it will correct the distortion. This worked for me, hope this helps!

DK64 like all Rareware games starting with GoldenEye 007 in 1997 supported true 16:9 WIDESCREEN native and dolby surround, infact some games such as GoldenEye featured a range of aspect ratios to play in. Nintendo did not support 16:9 for another 10 years, because they didn't have the technical skills to do so.

Judging by this it may take another 10 years before they add widescreen to their emulation.

It seems Nintendo have chosen the laziest option - apply one rule for all, a simple line of code in their emulator is all that is needed to allow gamers to toggle 4:3 fullscreen then 16:9 could be implemented in game menu as usual. As it seems 16:9 works in game but the Wii U still maintains the borders thus giving gamers a squashed image when enabled.

My original Donkey Kong 64 pal cartridges runs 16:9 widescreen without any borders.

I had the same problem on my Wii U.

Before I started the game I changed the resolution to 480p and set the ratio to 4:3 instead of 16:9.

It fixed both my problems with dk64 and VC games on my vWii

It's possible. Nintendo did it as a marketing scandal. There's a few things you need, (homebrew channel, a custom one with 16:9/full screen, a application called wiilauncher, I'll get the links later). Use wiilauncher, go into config setup hook none, switch aspect ratio to 16:9, save config, and launch channel once you leave config.

here is the tutorial bit, so first your going to need yawmm which is right here https://sites.google.com/site/completesg/how-to-use/wad-manager make sure you get the one with vwii support it will say it!!!! next is http://www.hacksden.com/showthread.php/7814-Workaround-for-the-HBC-with-the-latest-Wii-U-update this is the download page for the custom hb channel with fullscreen support, choose your colors, you got dark blue, black and yellow... is that.. ok anyways once you have those files put yawmm in apps folder if you don't have one create one. it needs to look like this when you open your sd card (you can have extra stuff but I mean make sure it exist this way) (apps) (YAWMM_EN) and somestuff within that. ok once you checked that is place properly, get your other file (it should be a .wad) and put it on the root of your sd, aka when you open your sd card in a file explorer and haven't moved into any other folders. last but not lest you need wiilauncher (sorry i don't have a good enough rep since i Just joined look it up, it should be in wiibrew . org or something like that when looking in applications, it description should be a alternative to gecko os (gecko os is a cheat manager thing, but i found out that using wiilauncher without cheats allows it to be run in fullscreen) ). Ok do the same with with wii launcher like yawmm. Ok get your sd card in your wii u run the homebrew channel, run yawmm, and install your .wad file, this is why I said root because its just easy to find it, once that is installed leave yawmm and leave the homebrew channel, you should see a new channel, which is the color you choose, use that homebrew channel, now at last, run wiilauncher, I recommend you change your config, the reason why is so if you do have cheat codes (somehow) it won't run them which is why putting the hook type to no hook (disables cheat codes in its entirety) and set the aspect ratio to 16:9 aka fullscreen. and launch channel. I must tell you this trick might not work for certain vc, such as sonic the hedgehog, but super mario world, mario kart 64 super mario 64 (just a lot) wil work, note this is for wiiu in vwii mode

In the Wii U System Settings, under TV there is an option for Screen Size at the bottom of the page, where you can adjust a slider to change the size of content on the screen. After some trial and error, I found that the 4th spot from the right was the best for my TV's 'Wide Fit' mode, and now vertical resolution is maximized without any cropping. There are still two thin black bars on the side, but I think that's just the nature of the content being made for a 640x480 aspect than a 720x480 aspect.