With SketchUp (SU), you can use precise dimension and many available units.
With your model, you can set the units to cm. You do that once.
Then, for example, you want a rectangle of 2 cm x 4 cm, follow these steps:
1 - Select the Rectangle tool.
2 - Click on the axes origin to start the rectangle.
3 - Move the mouse along the red axis, then along the green axis. You can also move on the red-green plane (ground plane) if you prefer. Don’t click yet.
4 - Type 2,4 or 2;4 (depending on your regional settings) then press the Enter key. There is no need to add cm after your numbers if you have set the units to cm.
You shall have a precise rectangle of 2 cm x 4 cm.
If to orientation is not what you want, retype 4,2 or 4;2 then the Enter key. The rectangle will change orientation.
As long as you do not exit the tool or change tool, you can type new values as you wish.
Now, If you absolutely need a grid, you can use guides set at every centimeter along the red and the green axis.
To get that grid, you establish a first on the move copies along the required axis.
See this SU file for ideas.
Grid 1 cm x 1 cm.skp (222.6 KB)
You can also use the Sandbox tool From Scratch to set up a grid although you might have difficulties using cm as the unit. You can use meters for example and scale down when done.
With more recent versions of SU (since you put 2017 in your profile), you could create a grid, then group it and assign a tag to it. Then you could set that tag to use dashed lines or even dotted lines.
Since I don’t know how this file would open in SU 2017, I post a jpg export here.
I think there are plugins to draw grids like you want.