Payment suggestions:
Checks for federal estimated tax payments should be made payable to the U.S. Treasury.
We recommend that you write your social security number on the check and write 1040-ES (and the tax year it is for) on the check. Some taxpayers are concerned about identity theft and are cautious about having their social security number on more documents than absolutely necessary. Make your own decision - keep in mind that your social security number will be on the form that your check gets mailed with. A point well taken that when the check is returned with your bank statement, your social security number is then on that check.
We default to suggesting that you pay the 4th quarter state payment by December 31. The logic is that you want to be able to deduct all 4 state payments on your federal tax return. If you are concerned about not having a tax benefit for such payment because either you do not itemize deductions, or because you are in the alternative minimum tax, just pay in on the January due date.
I (John) never bother to send these payments by registered mail or the likes but if you are more comfortable with that, by all means do so. I (John) suggest that you consider mailing the form a few days early and when you check your bank account on line, you should see these checks clear rather quickly.