How to fix compatibility issues of PS2 to HDMI and Wii2HDMI adapters
For people who don't have RGB SCART or component video inputs on their HDTVs, HDMI adapters for the Sony PlayStation 2 and Nintendo Wii are the simplest way of displaying these consoles on modern televisions. They are also the simplest way of recording from these consoles with capture cards that only support HDMI. The PS2 to HDMI and Wii2HDMI adapters take the YPbPr component video signal from these consoles and convert it to digital HDMI video. There is also a Wii adapter by Lenkeng, the LKV-6000mini, which does indeed upscale the image to 720p or 1080p.
But depending on which games you want to play, you may run into compatibility issues. Most modern HDTVs and capure cards only accept 480i or 576i through HDMI as their lowest resolutions. But PS1 games typically ran at an even lower resolution: 240p in NTSC regions, or 288p in PAL regions. Similarly, retro games available through the Wii Virtual console typically ran at these low resolutions. There are also some games like Driver that use 240p/288p for gameplay but 480i/576i for the menus.
If your HDTV doesn't support 240p or 288p over HDMI, the screen will just give you an unsupported format error message. And if it does support these low resolutions, they may have a significant blackout when a game switches between resolutions. Some Virtual Console games had a 'Component AV Interlace Mode' to get around these compatibility issues, but not all games supported this mode.
Fortunately, there is a way to overcome these compatibility issues. There is a SCART to HDMI upscaler that is readily available on ebay and Amazon. There is also an AV/S-video to HDMI upscaler by Lenkeng. Both of these external upscalers have a HDMI input that correctly recognize 240p and 288p, which you can use to upscale PS1 and Virtual Console games over HDMI to 720p or 1080p. For the PS1 games that do switch resolutions between gameplay and menus, Sony released an AV/S-video breakout adapter that you can use to send composite or S-video to the analog inputs on these scalers whilst simultaneously sending HDMI to the scaler's HDMI input.
While I personally prefer to use RGB SCART for PS1 and PS2 games, I feel the Wii HDMI adapters are the way to go for the Wii. But Virtual Console games that don't support the interlace mode will definitely cause compatibility issues and a lot of headaches for some. As will PS1 games played over the PS2 HDMI adapter. As a public service, I'm posting this video to help users of these adapters get around any compatibility issues.
NOTE: This video is an updated version of a video I posted on April 27 2018. My apology to everyone who left a comment.