Recently, I was working on a project that required cope and stick doors. To help me rout the end grain cleanly and quickly, I built the jig shown here.
The router jig consists of a plywood base that acts like a sled. I cut pair of large slots into the base of the sled using a forstner bit to create the rounded ends and a jigsaw to remove the bulk of the waste. These slots let you easily clamp the workpiece in place.
I also screwed on a cleat that accepts a backerboard (see photo above). Finally, I added a handle to easily guide the sled.
The jig functions as both a sled and a miter gauge. I clamp the workpiece to the jig and adjust the fence to the proper position for the router bit I’m using. The backerboard helps control chipout and can be replaced as needed. Then, it’s a simple matter of pushing the sled and workpiece past the bit.