"A kitemark says that way back when it was awarded, no obvious security holes were found. It does not mean that the site is secure."
Could it be made meaningful?
1. Requires regular 3rd party checking to a given standard, preferably including pen testing. Regular as at mandated intervals, say 6 monthly.
2. Date of last test shown on site.
3. Covered by insurance. Preferably no limit to amount insured.
4. Expiry date of current insurance shown on site. If the amount of insurance is limited this should also be shown.
This would mean that there would be at least two parties, the testing company and the insurers and maybe also the testing company's insurers standing behind the site's certification.
It could work, it wouldn't be cheap but it would mean that you'd be able to identify a site that took security seriously.
Self-certification? ROFLMAO