I know how to Ctrl+B then drag to manually create border while in camera view (Numpad 0). I also know I should check both 'Border' and 'Crop' in 'Dimensions' panel of the 'Render' context of 'Properties' editor.
However, I want to precisely create a tight fitting border around selected object like you can do in Inkscape when you "Resize page to drawing or selection".
Full disclosure, the add-on I'm about to recommend is a paid for add-on created by me.
'Animated Render Border', my add-on, allows the user to select an object from a drop-down list and automatically detect where the render border should be positioned so the object is encompassed by it:
You can choose whether it does this via the object's bounding box, or more precisely, using its vertices (if it is a mesh, curve, armature (uses bones) or lattice). It also has a mode to allow a more manual fine tuning ('Keyframe' mode).
As the name might suggest, this is actually intended for objects that are animated that you want to be contained within the render border, but it works perfectly fine for stills.
There are some limits in that modifiers that alter the object's geometry aren't currently supported and there are some objects which can't be 'tracked', like empties, lamps and cameras.
This is not available in Blender by default. It must be coded in python :(
Fortunately, its already been done:
https://cgcookiemarkets.com/all-products/animated-render-border/
Unfortunately, it costs $7 roughly.
Disclaimer: I don't own the add-on myself, but the Blender Market maintains a high level of discipline so I would assume it to be high quality and do what it says it does.
