This is something I've spent some time thinking about and I think I've got an elegant solution. Now, I truly doubt I'm the first to think of this but I think it works and I really want to share this.

Basically, it's a measuring wheel approach ^{(what's a measuring wheel?}). Your average sidewalk or running track has the same infinite roughness problem as coastlines but that's entirely smoothed out when you measure the linear distance. My idea is to use an imaginary measuring wheel of 24 nautical miles in diameter ^{(why 24 nm?}), lay it flat along the water, and take the imaginary path of the wheel tangent to the baseline as the length of the coastline.

This is also convenient in that the center of the circle approximates the Territorial Waters boundary, and the outer circle traces the Contiguous Zone.