I believe my coverage only lasts until my final day of employment
I'm thinking of getting some sort of basic emergency coverage, just in case I end up getting in a car accident on the way to CO or something...
1) Don't think like that.
2) That's what you have auto insurance for.
Can't stay, way busy today....
Most employers must cover you through the end of the calendar month. If you leave halfway through the month, your insurance should remain in effect until the last day of that month.
Insurance companies do not "pro-rate" their premiums. It is done month to month. My main concern would be the possibility of a double-deduction on your last paycheck to cover your contribution.
Double-check with your HR department though.
You can continue to pay premiums to your old job and keep your current coverage at the current rate for a year. It's called COBRA coverage, and your HR person will know how it works. If you have the cash flow to do that, it is very good piece of mind.