I'm working with footages that are shot handheld. The shakes are not too aggressive but they're still noticeable.
For the longest time ever I've been using Final Cut Pro's stabilization function to stabilize these types of footages, but the outcomes are always less than ideal.
What's a good way to deal with this?
Because software stabilization methods cannot compensate for the shifting parallax of a shaking lens, they will always produce less than ideal results. In my experience, FCPX's stabilization is just as good as other software packages (I have experience with Shake and After Effects as well), and they all basically work the same way.
This is probably not the answer you want to hear, but the best way to stabilize footage is to shoot stable footage in the first place. Software stabilization is really just analogous to fine grit sandpaper; It's a good final step to add polish, but you'd never use it from the start.
Physically steadying a camera can be expensive, but that's why audiences have learned to appreciate stable shots -- they associate stability with quality. But of course you know this, or you wouldn't be asking.
But there are good, reasonably priced ways to physically steady a camera. Where I work, we have dollys, sliders, shoulder mounts, tripods, brushless motor gimbals, camera cranes, clamps, arms, and pretty much you name it. But in my experience, the most versatile, portable, practical, and cheap piece of kit that we routinely use is a monopod. It doesn't allow for all of the fancy movements of the other stuff, but nice ones will at least let you do a fluid pan.
Sorry this doesn't help with footage you've already shot, but I hope it helps with future projects.
Motion 5 has more robust image stabilization tools. But ultimately, this issue is best fixed when you're shooting, not in post-production.
I don't have any indication from your post as to what subject matter you are recording and how much experience you have with video production. I'm going to assume that you are recording live action and from a distance. The best you can do is put the camera on a tripod as close to the action as you safely can, zoom it wide as possible, and keep the camera as steady as possible.
The unfortunate truth is that ultimately the best way to get steady footage is to record steady footage. Beyond this, however, there are plugins in many non-linear editors to fine-tune the stabilization. I've had decent results with the stabilization plugin in Sony Vegas. Some folks use After Effects.
What I do is I record lots of footage, use short clips where they're the most steady, throwing out pretty much all footage that's even slightly shaky. Usually, I can tell the story well enough without the shakier footage.
