My site handles sensitive data, is there any website security accreditation that is well respected and worth having?
If you want something that's immediately noticeable as a security change to the visitor, Google: "Trusted green browser bar", which for modern browsers turns most if not the entire browser address bar green (depending on the browser).
This is occurs when a site has a "Premium SSL" certificate installed, more specifically called an "Extended Validation Certificate". Just for reference, GoDaddy sells Premium SSL's with a $250,000 warranty. You can chose to use either GoDaddy or its security brand "Starfield", both of which will provide an HTML snippet to add a "Verified & Secured" graphic to the bottom of your webpages.
Aside from that, a standard SSL certificate with a login requirement (i.e., through a .htacess passwords file) should tell your visitors that you're quite serious about security.
Tip: Always check for discount codes when buying SSL certificates, as they can drastically lower the cost for the first year.
Here some "neutral information concerning "SSL certificates" and website security:
A SSL certificate provides a secure connection for your users as well as assurance to visit the "original" domain (See phishing).
A SSL certificate does in no way guarantee secure storage of data on the website/company servers, nor does it guarantee that the website/server is not exploitable.
Comodo offer a HackerProof "trustmark". This shows that the site has passed certain security requirements and is PCI compliant. Having some sort of security seal like this along with an EV Certificate (to give you that "green bar" in most modern browsers) should instil confidence in your users.
Additionally, having information on your site detailing what you do with sensitive data, how you store it, and why you handle it the way you do should make users feel safer providing it to you.