I am not sure carbon dating will work.
It is based on uptake of C14 by a living organism . As soon as the organism dies, it stops absorbing carbon at all and then we can measure the ratio of C14 : C12. From this number we can calculate the age of the remnant knowing the rate of decay of C14 into C12.
Metals are not living creatures. Alloys such as steel were prepared using carbon existing at the time of manufacture and the dating will reflect the age of, say, coal(several millions of years) or wood/leaves (days to tens of years). If I use coal made out of 500 yo wood (such as many olive trees), the sword made in 2005 will reflect the age of that particular wood.
Also, the precision of the method is too crude to be of major help to us: it is relatively easy to distinguish an object that is 2,000 years old from the one that is 100 y.o. However, we are mostly interested in "is it 19th or 18th century?" type of questions. That falls well below the assay limit of resolution.
Ann Feuerbach would know the answer much better and correct me if I am ignorantly wrong.
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