What the W3C says (not required)

You do NOT need a conformance claim. The W3 states specifically that conformance claims are optional.
 
Note, if your website is non-federal (not a federal agency or recipient of federal funding) then Section 508 compliance is likely not required, which makes a conformance claim unnecessary even more.

What you need to provide a conformance claim

If you or your organization does choose that a conformance claim is needed then there is a simple set of criteria of how this should be documented.
 
The following must be provided: Date (I recommend a full timestamp), Guidelines (i.e. WCAG 2.0), Conformance Level (A, AA, AAA), full URI list (pages that have been audited and approved), web content technologies used.
 
There is additional information than can be provided, which is optional, but I’d recommend providing as much of it as possible. The reason behind that recommendation is that the claim is not required and so the providing of it is purely to provide evidence of a proactive and thorough accessibility strategy to help mitigate potential lawsuits or complaints.
 
The full list of Compliance Conformance: https://www.w3.org/TR/WCAG20/#conformance-claims

Partial Compliance Claims

It is worth noting that Partial Conformance Claims [https://www.w3.org/TR/UNDERSTANDING-WCAG20/conformance.html#uc-conformance-claims-head] can be made. The W3 states “…if the page does not conform to WCAG only for reasons that are legitimately outside the author’s control then the author can make a claim of partial conformance.” This is an important statement as it both understands that claims achieve no absolute legitimacy for full conformance and that there are legitimate reasons why.

Why I recommend to avoid making a claim

I have no legal background and am not providing legal advice, but from what it appears the United States has an “adversarial” legal model. This is perhaps why the Miranda rights are required to be read/spoken in some instances… maintaining the choice to “not speak” is often a good option in an adversarial system.
 
By listing a conformance claim you’re choosing to NOT maintain your right to remain silent and for no obvious benefit that I can see. The more information that you divulge the more potential ammunition you provide to an accuser. I’d recommend to do what’s recommend and keep that documented internally.

Make an “Accessibility” page

A trend I’ve been noticing that I believe is a great solution is the provision of an Accessibility page. An accessibility page is typically positioned in the Footer of a website (not main navigation) and included a brief description of the company’s position on accessibility along with a way for accessibility complaints to be submitted.
 
I believe this is a great solution. It creates a proactive approach, proves accessibility concern, and mitigates future issues. It’s not bullet proof, but a huge step in the right direction.
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