Newer versions of iMovie have a Stabilization filter. It’s one reason (the only one I can think of) to use iMovie, but it’s a good one.
1. Import the source file (iMovie copies it into the project, unlike FCE/FCP, which only references the clip).
2. Drag the clip (or some part of it) from the Events to the Project Browser window.
3. Choose File/Analyze/for Stabilization. Then double click the clip and select Stabilize, or Smooth (I forget).
4. Export (under Share menu) “using Quicktime.”