There might be a better way to do this, but if you go to the Form 2210 Underpayment Penalty Worksheet, you can go to the 4th quarter and override the "days late" (subtract 31 days).

I would just enter the payment date as the start date of the disaster relief period.  How it works is the time between the disaster start date and the relief expiration date is "disregarded" for penalty calculations.

Rick

Good idea.  And after reading your comment, I realize my answer would give a wrong result, so thanks for the correction.

Thanks all for answering.

Yes. I had changed the date of the payment to Jan 16th (from Feb 15th) in order to make the system think it was timely and I believe that works. I'm a little concerned about the IRS sending a notice on this and it seems that there ought to be a way of notifying the IRS that taxpayer is claiming exception due to a disaster declaration. 

Oh well ... what's a few more IRS notices.

I've been assured by IRS personnel that relief will happen automatically.  That's somewhat tongue-in-cheek but that doesn't make it less true.  I've also been assured by IRS personnel in the past that every CP-2000 letter is reviewed by a human before it goes out.

If you're unlucky enough to not have been picked up by the automated "disaster by zip code" system (or, for example, if your books and records are in a disaster area but your mailing address is not) you can self-identify by calling 866-562-5227.

Rick

Edit: I'll tack on the FAQs for posterity:

https://www.irs.gov/businesses/small-businesses-self-employed/faqs-for-disaster-victims