Accuracy of Dating Artifacts?

To answer your question, carbon-14 dating actually dates the point in time at which the object or material in question stopped exchanging carbon isotopes with the outside environment. This usually occurs when the organism dies. C14 dating wouldn't be done on a rock, but it might be done on charcoal or plant material found on a rock. The age of the rock doesn't really factor in at all.

One early assumption about C14 dating (or any radioactive dating method, for that matter), was that the rate of exchange between organisms and the environment is a constant, and has been constant for a long time, or forever, making the dating process very straightforward. This is not the case unfortunately, and so using C14 dating alone will give increasingly inaccurate dates with the age of the material. C14 must be calibrated with an absolute dating method that allows the identification of carbon-14 content or exchange rates at a given point in history. This can be done, most commonly and reliably using tree rings or varves, which contain organic carbon from known points in time. Unfortunately (again), carbon exchange rates also vary regionally, and so some parts of the world have better calibration curves for C14 dating than others. Some go back thousands of years, some only hundreds, so the quality of C14 dates can vary from place to place around the world.

Furthermore, C14 dating is theoretically useful to date objects 30,000 years or younger, but very few calibration curves, if any, go back further than 5000 years. This isn't to say that nothing is older than 5000 years old, just that C14 dating generally loses a lot of its control past that mark. An artifact dated to 18000 years old could have a wide margin of error. Fortunately, we have lots of other dating methods that cover a varied range of dates. The process for C14 is just so solid and direct, and it's tailor made for organics, it's a shame that calibration is necessary.

We don't do carbon dates on lithics or ceramics, usually. What we do is carbon-date things like charcoal or plant material. It's not perfect, as sites are almost always disturbed. The charcoal sample you pull might be from a fire in the hearth you're investigating, it might be a decayed root, or it might be from the forest fire last year and a rodent burrow caused it to get into your feature. But often, you get some samples that are from the appropriate time-frame. If you pull samples from several firepits around the site that all confirm a date of 6,000 years ago, it looks pretty good.

And it's not just c-14 samples that help us determine dates. The soil layers around the US are pretty well documented, so they can be a pretty useful way to figure out how old something is. This is part of the reason that where something is found is even more important to an archaeologist than what, exactly, it is. Also, we've got a pretty decent picture of what styles of artifacts were around when. If you find a complete arrowhead (has to have the barb, not just the point) or a decorated piece of pottery, you can probably get a good date range. If you've ever heard of the Mississippian, Archaic, or Paleolithic eras of US prehistory, those are pretty much defined by artifact styles and types. So if you're pulling classic Archaic points out and your carbon samples are giving you a date of approximately 5000 years ago, you're golden. The artifact style and the samples both show you're dealing with an Archaic site.

Ceramics are dated NOT by carbon 14 - but by thermoluminescence. TL measures the date that the object was burned (fired in a kiln), and NOT the age of the clay itself.

Carbon 14 is only good for measuring the age of biological materials. For example, if the people ate some deer, we could use carbon 14 to date the remaining deer bones. If the people HAPPENED to be carrying around 5,000-year-old deer bones, it might cause some confusion.

However, the age of a site is not determined by one date alone. Its context, along with its content, its stratigraphic location, and multiple dating methods, are needed to ensure accuracy.

Even low-budget projects usually request at least 3 different C-14 samples from 3 different areas.

Of course, no one method is 100% fool-proof. For example, counterfeiters have been taking bits of (valid) pot sherds and grinding them into powder, reshaping them into (more valuable, but fake) "pottery statues." In this case, the TL tests DO show that the object is "old" because they reflect the age of the original pot sherds.

This is another reason why good archaeologists never rely on one line of evidence to support a claim.

Carbon dating would not be done on a stone or ceramics, as you are suggesting. Carbon dating is done on organic substances. For dating ceramics and other non-organic substances, the dating would be determined by the time period that the particular style of the artifact was being produced. You can also narrow it down based on other artifacts found with it. For instance, say you find an artifact that was produced between 1500 and 1600 beside an artifact produced between 1550 and 1625. Since Artifact A wasn't produced after 1600 and it would be impossible for Artifact B to have been dropped there before 1550, both artifacts would date to roughly beteen 1550 and 1600. Sometimes you get lucky and get an artifact with an actual date on it (coin, certain ceramics) but this is a rare occurance at best.

C14 will register the item in question only, the latter wil depend on Anthropologists and Historians on how they put the story together.

Honestly i don't think this question will ever be answered in a satisfactory manner.