- Disable JavaScript and use your website. This may not be relevant for web apps, but regular websites should work normally.
- Try to use your website with only the keyboard.
- Try to use your website with extreme zoom levels and font size overrides.
- Monitor your resource sizes. Anyone with a limited connection (a LOT of people) will abandon your website because it loads slowly, or are paying actual money for the wasted bandwidth.
I'm not aware of automated methods that give better results than using your website with the actual accessibility tools yourself.