If there will be less than 60 days between the time your insurance benefits end at work and you're eligible for student health insurance, you can also just wait it out and see if you incur any medical bills. If you do, you can elect COBRA, pay the premium, and your benefits will apply retroactively. It's just critical that you're within the 60-day window that you're eligible to elect COBRA.
Also, check your HR policies on when coverage ends. At a lot of companies, it ends on the last day of the calendar month in which you leave the company. I'm planning on leaving a couple days into June so I will have coverage for the entire month. Then I'll just be uninsured for July and August, but by August I'll be eligible for student insurance, so if something happens between those two points in time I'll elect COBRA.
There's some good info here: http://articles.moneycentral.msn.com/In ... spx?page=1
The 60-day retroactive part is on page 2.
Disclaimer: Talk to your HR department about all the details and how they work at your company before you leave. Health care laws are rapidly changing, and this isn't something you'd want to screw up.