Dating using measurements of the isotopic $^{14}$C/$^{12}$C ratio can be done even for quite recent dates, but the principle is different to the standard radiocarbon dating.
The method is known as bomb pulse dating and owes its efficacy to the large amount of $^{14}$C that entered the atmosphere as a result of the testing of nuclear weapons in the 1950s and 1960s.
The $^{14}$C atmospheric abundance peaked in the early to mid-1960s at around twice the longer-term average and has since declined pseudo-exponentially with an e-folding time of around 15 years. From the wikipedia article I referenced, it looks like there are some (smaller) geographic variations too.
Because the half-life of $^{14}$C (5730 years) is much longer than this, one can essentially assume that the amount of $^{14}$C in a recent biologically-based sample reflects the amount of $^{14}$C that was present when it expired.
A review article by Grimm (2008) discusses this technique and gives examples of how it has been used to date biological specimens from the 1980s and have enabled estimates of birth dates for corpses by looking at the $^{14}$C content of tooth enamel. The article points out though, that because of the gradual reduction in $^{14}$C back towards its "natural" level, that this technique will not work much beyond 2020.
There are numerous applications of this technique - from dating human cells and cancerous tumours to figuring out when illegal drugs were harvested.
The same phenomenon really precludes using traditional radio-carbon dating over the last 50 years, however, prior to this it appear that the behaviour of atmospheric $^{14}$C was much more constant - to a few percent (see below, from Giem 1997, adapted from Stuyver & Becker 1993).
Given this, I see no reason why radio-carbon dating cannot be used for material that is 500 years old, since that should result in a $^{14}$C/$^{12}$C ratio change of order 10 percent which is several times larger than the natural variation. However, if I interpret the plot above correctly, because the natural $^{14}$C fractional abundance was decreasing between 1550 and 1600 (and perhaps before this too?) at about the same rate as the radioactive decay rate, this leads to an ambiguity in the age determination and then there would be at least a 50 year uncertainty in any radio-carbon age from about that time, even with very precise measurements, but you could reasonably confirm that something was at least 350 years old.
But then you see that beyond about 1700, the trend and magnitude of the change in the natural $^{14}$C almost mimics the radioactive decay curve, so it must be very difficult to age anything younger than this in an unambiguous way.
