It's difficult to understand what you mean by stuttering (is the camera panning too fast? Or is there tearing?), but here's a way to implement smooth camera movement.
For the sake of simplicity, I assume your camera has two variables cameraX and cameraY which determine the camera's position.
Add 2 new variables, cameraTargetX and cameraTargetY.
The idea is, every time the mouse moves the camera, instead of modifying the variables cameraX and cameraY it will move the cameraTargetX and cameraTargetY. Then in your Update you modify the value of cameraX and cameraY to get closer to cameraTargetX and cameraTargetY like so:
void update() { cameraX += cameraTargetX -cameraX *0.5; cameraY += cameraTargetY -cameraY *0.5; }
This will cause the camera to move half the distance towards the target every frame. This is only an example, you can make a custom formula depending on how your game currently works, but hopefully this is enough to show a method of achieving this.
I wonder if there is a generally agreed upon way of doing this?
In general with game development, there's multiple ways of doing things. As long as you get the desired result that runs with acceptable resources, you are good to go.