The intent is to avoid an underpayment penalty by making the payment for the same tax quarter as the tax quarter in which the income was received, not to pay the tax and possible penalty with the tax return.
Once that you've determined using simulated tax returns that you might be subject to an underpayment penalty, to make a state estimated tax payment, go to your state's website to find the information on making an estimated tax payment. You can also consider increasing your state tax withholding from other sources throughout the year to make up the difference.
