My hypothesis is that that US coins, and especially pennies and nickels, would retain most of their current value, despite a hyperinflation on the US dollar. Here are a few reasons:
1. The metal (melt) value of coins, especially the penny and nickel, is very close to their face value, and in fact, the metal value of both exceeded their face value in 2007.
2. In Zimbabwe in 2008, hyperinflation increased caused the bills to get so many zeros (e.g. billion dollar bills, trillion dollar bills) that they eventually said, okay, 10,000,000,000,000 is now equal to 1 new dollar; but the 1 dollar coins, although they probably disappeared from circulation, were reintroduced after the revaluation... as still being worth 1 dollar. That is to say, that 1,000 ZWL in coins in 1980 would buy the same amount as 1,000 ZWL in coins in 2008.
Old coins from the first dollar in the values of 10c, 20c, 50c, $1, $2, and $5 became legal tender taking the value in new currency(thus, effectively increasing their value 10 trillion-fold)... -- Wikipedia
3. In current Argentina, the coins were more valuable than the bills (at least for a time), due to a coin shortage, but also perhaps due to the hyperinflation that Argentina had experienced.
4. During a hyperinflation, the coins may or may not be valuable during the event. It may not be until after the event that they are valuable again.
(The link above suggests sorting the pennies into the copper (pre-1983) and the newer zinc/copper kind, and then going back to the bank to get more to sort. As for nickels, those seem to be popular for collecting or hoarding.)
In preparing for hyperinflation, it seems that a small investment in metal coins, particularly pennies, nickels, silver and gold coins, inspires a bit more confidence than paper bills. Time will tell.
This is a quite amazing video that literally gave me chills a number of times, because it is so real, and happening now. It a very scary look at the state of the economy in Zimbabwe, where the money is now totally gone, and people are panning for gold all day to have enough gold to buy a loaf of bread for themselves, and those who do not pan, particularly the old, are without any means at all to sustain themselves.