Web design is not a regulated industry such as law, medicine, accounting or engineering. That's why there's no requirement for you to get a web design license in order to practice web design.
Secondly, the W3C offers no certificates for web design or otherwise. W3School offers one, but they're an unrelated commercial organization that has no regulatory authority and are not professionally or academically recognized by anyone.
CWP and WOW are both equally worthless certificates. Judging by their websites, at best their certificate guarantees that the holder is familiar with web development technologies/methods that are at least a decade or more out of date. At worst, it strongly suggests that the certificate holder probably has no clue what they're doing, which is why they'd be taking web development courses from organizations so far removed from the professional sphere.
If you want to learn about web development, you should take courses at a university and participate in events and organizations put on by the web development community. BarCamp, An Event Apart, FOWA, FOM, RubyConf, jQuery Conference, JSConf, ZendCon, Full Frontal, etc. are all great places to advance your education.
But web technologies are always evolving, and that's why there's not much point in a certificate for web professionals. Anyone who thinks like that will quickly find their skillset out of date and obsolete. Instead, professional web developers are constantly learning and developing their craft, picking up new technologies, experimenting with new methods, and keeping up with ever-evolving best practices. And this style of learning is much more suited to bootcamps, conferences, and self-study rather than a static certification process.
Lastly, you mention web design, but you named certificates that have to do with web development, and that's a fairly common mistake to make. However, web design and web development are two different things. Many front-end developers are also designers, but they're two separate disciplines that each require a lot of effort/attention to master and stay up to date on. So unless you're willing to make the commitment to basically work 2 full-time jobs, you should really consider specializing in one or the other. Because most of the time people who don't distinguish web design from web development tend to do a very poor job of both.