There's a great app for iPhones called "Motion Stills". It can make a handheld "Live Photo" with a minimal movement, totally stable. You can see original Live Photo here and edited with the app here.
The only problem is that the application works only with previously mentioned iPhone's "Live Photos". Can I find there any program for Mac to make the same results with videos? Is it possible in Adobe Premiere?
You should be able to use any software for video stabilization. With ffmpeg you can use either deshake, or vidstabdetect/vidstabtransform.
Depending on how shaky the original video is, you can get rid of the black distracting margins by zooming with the zoompan filter, or cropping with the crop filter. See the links for examples.
You'll probably have to experiment a bit to find out what works for your material. Use ffplay with the same syntax to see directly how the filters work.
There are differences, firstly, between still and stable. If you want a video to be still, as if it were filmed on a tripod, then you can use a tracking stabilisation technique. This is when you track a point in the background, and since the background is meant to remain motionless when on a tripod, the computer can compensate by moving the video in the opposite direction to the motion. By zooming in, you can remove the bars at the side that would appear from moving the image out of the screen.
However, if you want steadiness, where the camera still moves, but without violent shaking, such as if you were using a Steadicam, and have the privilege of using professional software such as Premiere, there are methods to achieve this. In Premiere, you can use the 'Warp Stabiliser' effect, and if you ensure that the 'effect' drop-down is set to Smooth Motion instead of No Motion, you should be good to go. But remember that if there is too much shake in the camerawork, Warp Stabiliser could make it look even worse. If you do not have access to Premiere, you can use the previous technique of removing motion completely and adding something like Cinecom's handheld camera effect package in Hitfilm to simulate handheld motion, smoothly.
The effect in Premiere you want to look for is the warp stabiliser effect: https://helpx.adobe.com/premiere-pro/using/stabilize-motion-warp-stabilizer-effect.html
As mentioned, this works by moving the video frame to try to keep the contents of the frame in the same place on screen. Obviously this means that the edges of frame become visible, meaning you need to crop or scale to hide them.
Another problem that is a bit more subtle is that perspective and parallax gets messed up by over-use of stabilisation. When you move the camera the position of foreground items to background items changes. If you then take out the movement you're left with the relative motion of the foreground and background, with nothing to explain it.
On top of that, any rolling shutter artefacts will remain, once again, without any motion to explain / mask it.
This can leave you with a steady frame that looks like it's made of jelly, which is really disconcerting. So don't expect motion-stabilisation to be a fix for bad camera work.
