Is it worth backpaying a missed quarterly tax estimate payment?

I want to perform payments in addition to my standard withholdings. However, I missed the Q3 deadline (9/15). Is there any point to still making a payment for Q3 after the deadline? (i.e. paying both Q3 and Q4 payments now)

Get your taxes done using TurboTax

Sure you can pay any amount you want.  It really goes by the date you make the payment.   When you enter the payments in next year you enter the date you paid.   So the sooner the better to avoid interest or penalties.   It may make a difference.

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Get your taxes done using TurboTax

One thing I pulled out of your answer was interest. So if I am penalized, I will avoid further accrued interest by paying now?

Get your taxes done using TurboTax

Correct ... it can reduce or eliminate the interest.