I'm looking for a solution to do screen recordings off of retro computers. The most straightforward way seems to be using a VGA to HDMI adapter, then connecting that to an HDMI capture card.

Contrary to what continuum says (he's usually spot on, though), it's quite normal for a HDMI to VGA adapter to be fairly warm. Ballpark figure for a HDMI to VGA decoder is around 200 mA at 5 volts.

It's pretty much impossible to find a display (or any consumer electronics made in the last decade, for that matter) that ...

An Apple spokesperson told The Verge that Lightning to HDMI and Lightning to VGA cables “will be available in the coming months.” by Sean Hollister Sep 13, 2012, 4:07 PM PDT ...

Many years of using televisions, monitors, and projectors have conditioned us into treating them as simple peripherals whose cables carry only video. A VGA cable may have an i2c interface for monit… ...

However unlike the Wisair device, which only output to HDMI, the Atlona Technologies adapter has both HDMI and VGA outputs, offering more flexibility for use with displays, HDTVs and projectors.

VGA isn’t as good as HDMI because of its lower-resolution video quality. It also only deals with the video signal, so you’ll need a separate cable to handle the audio.

Sometimes, you'll see a dongle or adapter that has both an HDMI or VGA port on it. These dongles connect up to your Surface just as we described above, but they have a spot for multiple monitor ports.

For instance, it offers adapters for VGA, DisplayLink, DVI, and HDMI. Some require USB 3.0—a good choice for gaming, graphic design, or HD video.