How do I determine what date my taxes are considered paid? is it the date I mail a check to the IRS? if I pay using EFTPS is it the date that I submit the payment?

Estimated taxes were underpaid, documents required to complete the tax return are not available and might not be available for a long time. I want to pay based on documents I do have and my best guess for the rest to reduce the penalty for underpaid estimated taxes so I will file for an extension and make a payment. When get all of the documentation and complete my taxes, what date do I use as  the date that the payment was made when I calculate the penalty?