Yes, you will owe a late-payment penalty for underpayment of estimated tax if you were required to make estimated payments and failed to do so, or failed to pay the required amount by the payment due date. You may be penalized even if you are receiving a refund. If your Illinois Income Tax exceeds the total tax withheld and credits by more than $1,000 you may have been required to make estimated payments. The late-payment penalty amount is based on the number of days the payment is late.  Payments less than 31 days late are penalized at 2% of the amount due and payments 31+ days late are penalized at 10% of the amount due. 

See Computation of Penalties for Individuals.

Hi,

Thank you for the prompt reply. I did not receive any notice that I was withholding too little, or I was required to make estimated payments, or to pay a required amount by a certain date. When I did my 2020 returns, Step 10 of my Illinois return (Underpayment of Estimated Tax Penalty) was blank. Does this mean there is no penalty and I just need to pay the underpaid amount?

Thanks

If you have a balance due, it isn't necessary mean you have to pay underpayment penalties. However, you stated that your underpayment for Illinois is about $5,000. In that case there should be penalties. 

Is there somewhere I can pay the estimated tax penalty online?

@andymartin54 

Since you are asking in a post about the State of Illinois.

Here is a link on where you can make payments.

https://www2.illinois.gov/rev/individuals/pay/Pages/default.aspx

Mote info About MyTax Illinois

https://www2.illinois.gov/rev/questionsandanswers/Pages/860.aspx

Q. Is there somewhere I can pay the estimated tax penalty online?

A. No.  Not exactly.  You cannot make a payment specifically for the underpayment penalty.  You can make a regular quarterly estimated tax payment and include an estimated amount for the penalty.  Any payment you make will  be applied to income tax, which will reduce the amount of the penalty.

@andymartin54   Did you get a bill for it?  You only pay an estimated tax penalty separately if you got a bill from the IRS or state if you owe more than was listed on your tax return.  Otherwise it may be listed when you file your 1040 or state tax return.