If you file the long-form Form 2210 in which you have to figure out
exactly how much you should have had withheld (or paid via quarterly
payments of estimated tax), you might be able to reduce the underpayment
penalty somewhat, or possibly eliminate it entirely. This often
happens because some of your income comes late in the year (e.g.
dividend and capital gain distributions from stock mutual funds)
and possibly because some of your itemized deductions come early
(e.g. real estate tax bills due April 1, charitable deductions early
in the year because of New Year resolutions to be more philanthropic)
etc. It takes a fair amount of effort to gather up the information
you need for this (money management programs help), and it is easy
to make mistakes while filling out the form. I strongly recommend use
of a "deluxe" or "premier" version of a tax program - basic versions
might not include Form 2210 or have only the short version of it.
I also seem to remember something to the effect that the long form
2210 must be filed with the tax return and cannot be filed as
part of an amended return, and if so, the above advice would be
applicable to future years only. But you might be able to fill
out the form and appeal to the IRS that you owe a reduced
penalty, or don't owe a penalty at all, and that your only
mistake was not filing the long form 2210 with your tax return
and so please can you be forgiven this once?
In any case, I strongly recommend paying the underpayment
penalty ASAP because it is increasing day by day due to
interest being charged. If the IRS agrees to your eloquent
appeal, they will refund the overpayment.