There's a new trail under construction at Seminole Canyon, it's listed on the map as "Proposed Hike/Bike Trail", and is now about 90% complete. I walked it this past weekend; you can access it about a half a mile down the Rio Grande Trail, the first chance you get to turn off to the left and just over the ridge that marks the 1882 rail grade you'll see a large cairn of rocks (about 4-5 feet high). From here, you follow the trail that hugs the top rim of the canyon until it meets back up with the Rio Grande Trail several miles just before the first picnic table overlooking Panther Cave. This part of the trail is not specifically marked, other than some rock cairns, but it is cleared of loose rock and very easy to follow. It follows along the edge of the canyon, so not much elevation change, and also much more interesting views than the Rio Grande Trail (which is mostly a featureless desert slog).
From there, follow the Rio Grande Trail the last part of a mile to the end, where a new trail continues along the edge of the Rio Grande, then loops back to re-connect with the Rio Grande further up. This trail is only about half-finished, the last part only marked by scant red ribbons in the vegetation. This loop is about a mile long, then after reconnecting with the Rio Grande Trail, just follow it back to the starting point.