Mirror workflow?: positioning 3dC at semi-circle's notional "center"?

When working with the Mirror Modifier I often want to scale something, like a neck segment, from the X-axis line, but w/o moving those verts on the X-axis at all. These shapes are often semi-circles with the flat ‘edge’ (no actual edge exists) on the X-axis.

What’s a good workflow to position the 3D Cursor at the “center” (not actually the center, not the median) of such a semicircle?

To illustrate, imagine a dragon neck , or a swan neck, and I want to scale just one of the (mirrored) rings.