You can pay estimated federal tax online whenever you want using
EFTPS. No additional cost for EFT payments, small charge for credit card payments. For state, check your state's department of revenue site. Some may allow you to pay online for a small fee (to cover the credit card processing).
Generally, as long as you don't have a balance due, and pay in enough each quarter to cover the tax liability (i.e., avoiding estimated tax penalties), there's no penalty for late filing of income tax forms.