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OmniGraffle's built-in lines don't do this, but you can attach shapes to the midpoint of a line. (Shapes can be line labels, in other words.)

I've attached a stencil Joel and I put together with a couple of examples. Instead of using the line tool, drag a line onto the canvas and snap it to the appropriate shapes. Does that help?
Attached Files
File Type: zip midpoint (2.2 KB, 265 views)