The Ukrainian national Bank recently announced it would like to stop issuing coins of one and two-kopecks (http://www.ukrinform.ua/eng/order/?id=182513) because according to opinion polls these coins have lost their usefulness. Given that people lose and destroy coins, stopping to issue a coin basically means gradually eliminating the coin altogether.
Many countries have eliminated small denomination coins before, and often such initiatives generate lots of discussion – Wikipedia has a good summary on the US debate, including on two bills on eliminating the 1 US$ cent coin, that were proposed to the US congress but that never passed.(http://en.wikipedia.org/wiki/Efforts_to_eliminate_the_penny_in_the_United_States).
One common cause of popular worry in these discussions is the alleged price increasing effect, the idea that shop owners will use the opportunity to increase prices up, instead of rounding up or down the price to the nearest 5 kopeks. Or that, because many prices end on .99 and few prices end on 0.01, rounding up will be much more common than rounding down. Academics have had heated debates about this second effect (see for example http://college.holycross.edu/eej/Volume27/V27N4P433_442.pdf and http://college.holycross.edu/eej/Volume33/V33N1P139_146.pdf)
Both effects would lead to a (one time) surge in inflation. But academics agree that overall, the effect on inflation would be very small for all but the lowest priced items: an increase of a price say from 9.99 to 10 would only be an increase of one hundredth of a percent. For the US, one study estimated that eliminating the 1$ cent coin would increase overall inflation in the US by one hundredth of a percent, which for all practical purposes is negligible.
Given the inflation levels in Ukraine, the proposal to stop issuing new 1 or 2 kopeks coins looks very timely as since the introduction of the UAH in 1996, 5 kopeks now are about as valuable as 1 kopek in 1996. Moreover, the price of stainless steel (which is used to make the one and two kopeks coins) is again increasing after a serious drop last year, making it more costly to produce such coins. I haven’t seen estimates of the cost of producing UAH kopeks but for Canada, academics have computed that the cost of producing a 1 cent coin is more expensive than 1 cent – see http://economics.ca/cgi/jab?journal=cpp&view=v29n4/CPPv29n4p511.pdf - for the US, recent numbers suggest the same http://college.holycross.edu/eej/Volume33/V33N1P139_146.pdf.