How fast is a serial port on a cisco router?

You have to be more specific when you are talking commercial cisco routers. It greatly depends which particular serial port you have. Some are very slow like the async ones designed to connect to old style modems. I hope you are not calling the console or aux port a serial port.
 

As bill says, Async or Sync? Sync only happens in the commercial world, business also use DEDICATED private links between sites without having to go through the Internet. I feel you haven't gone beyond a couple of chapters on your CCNA. Your work then doesn't sound large enough to use the "big boys" facilities.
 


Thanks for your god complex salt.