No, there aren't any real certifications or anything that an employer can use to verify your web design skills.
The best way to communicate your qualifications is to simply do some quality work (whether for a real client or a fictitiousone)and present that to prospective employers.
A key point to remember is that, regardless of your qualifications, the way you describe them will greatly affect an employer's perception of your skills (and your salary).
I would shy away from the "web designer" label and look to a more specialized area of web development like Information Architecture, Usability or the more all-encompassing User Experience. Many larger organizations have entire departments devoted to these areas, so entry level positions are often available.
These more specialized areas involve developing a strong understanding of the company's business goals and objectives. That is something that many "web designers" forget about, but it is crucial to your success within the organization. You must be able to demonstrate how your work directly impacts your department's/company's bottom line.
If you can go into an interview and show the employer how you can improve their business, you will be perceived as infinitely more qualified than the candidate who only focuses on their web design skills.
Hope this little rant is helpful.
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