The other option would be to rebase the currency such that a single penny was a meaningful unit of money again. One potential such way would be to issue new paper notes which represent the old note with a decimal place move such that $10 becomes $100. This has been done before but might not be a great idea for the USA.
That would be a nightmare, you're basically bringing in a new currency at that point because now all cash, every bank account and every price in the whole country needs to change. That's going to be probably hundreds of thousands of times more effort and expense than phasing out pennies!
I guess a reason to discontinue the penny is that it supposedly costs 3+ cents to mint one. I guess a nickel costs like 13 cents, though. I thought it would've been a better move to discontinue printing the nickel then just make all pennies worth 5 cents.