I had that happen to my ImpalaSS when I put a flowmaster dual system on it. The welder did a crappy, crappy job. There must have been 10 pounds in weld material added to the car.
I walked into the bay just as he was finishing up and said, "WTF???"
I walked into the manager's office (I knew the guy) and took him out to the bay. Not only did he have the guy re-do it but when the guy was done (and he did a much better, cleaner job the second time around), the manager fired him...
Using clamps will work if you get the right ones and are able to adequately seal the joint. Also, tighter is not better. Don't over torque the clamps. If you go, it will crinkle the pipe and create more areas for leaks.
If ya don't want to constantly chase exhaust leaks and there is no good welder around, use a band clamp. Here's an example:
JEGS Preformed Stainless Steel Exhaust Band Clamps - JEGS
These are much more expensive but they do not leak and you'll tend to see high end/high horsepower builders (Foose, Strope, Lingenfelter, Hennessey, etc...) use these:
JEGS Stainless Steel V-Band Clamps with Steel Collars - JEGS
Some folks advocate using a putty on the pipe area to be clamped. I've never used it but folks who do say it removes the potential for a leak at a clamped connection.
Exhaust System Repair : Permatex® Muffler & Tailpipe Putty