We issued a Form 1099-C to a company to cancel a debt. How do we enter this loss?

It depends on your accounting method.  If you use the cash method of accounting, income is included when you receive it and expenses are taken when you paid it.  Using the cash method, you never received this money and therefore never would have included it in income.  The 1099-C becomes income to them, and your deduction was already taken in the sense that you never included the income in the first place.

However, if you use the accrual method (which I suspect you do), then you write off these expenses as bad debts.  The accrual method includes income when it is credited to the account, which means you would have included the amount in income in a prior year.  When that amount is never paid and the debt becomes stale and canceled, you may write off the canceled (bad) debt as an expense against your income.