In 2015 the Smithsonian Air and Space Museum restored the original USS Enterprise model from the original series. It was built in 1964 by Richard C. Datin, Jr., Mel Keys, Vernon Sion (above), and Volmer Jensen (not pictured). It's 11 feet long and has been restored 4 times.
Trekmovie.com covered the most current restoration, which attempted to correct a problem with the third restoration:
That  restoration was actually quite accurate, but the restorer applied the "weathering" overlay too heavily," Mike told TrekMovie. "That's actually a very easy mistake to make. It's really very hard to judge the "proper" amount of weathering, especially for an object that is normally seen in second, third, fourth and worse generation photo images, which is what was done for the original optical effects. Nevertheless, I agree that the weathering was too heavily applied."
Mike says that the Museum may decide to take a more conservative approach this time around, saying "I don't think the museum has yet decided on the exact approach they're going to take. They're still studying it, trying to figure out a balance between restoration and conservation. They will want guests to see the starship in all its glory, but at the same time, they want to minimize invasive procedures in the interest of preserving the artifact (including its paint) for future study."