I have a Jenn-Air range top/grill that vents down through the basement to the outside wall. Part of the ducting is exposed but some is very hard to get at. Lately when I've been grilling steaks, my smoke alarm in the basement goes off and I can see the smoke in the air but I'm unsure of where the leak is. Is there a method to find where the leak is?

Yes draw some smoke into the Jen Air and look to see where it is coming from.

There is no other test that I can think of unless you can see the loose fitting. You may want to check the outside discharge fitting. There usually is a flapper door on the unit and if it sticks closed it will cause the same problem.