[Stiglr]

If you do a standard mirror, it will place the new parts amongst the old ones, leaving you to move it into place (and introduce error!) manually.

Object>Mirror --> X Axis is your ticket if you're working with the standard front, LEFT side and Plan/TOP views.That will produce a new half in the proper position, on the other side of the Z axis line.
To make it all mate up right, and to make ONE part of any part that lies right along that Z axis, you have to Snap Together (or "weld") all the centerline vertice pairs. If you are EXACTING in your creation of the halves, and can be sure that the vertices are right on the center Z line, you can make one "Snap Vertices by distance" command with a small tolerance, like 0.0005, and provided all the centerline vertices are right on top of each other, they'll join up in one fell swoop. But if there's any close detail at the centerline, of vertices that should not be snapped together, then you have to be more careful.