Square Top Mountain is sequenced with Argentine Peak. One way mileage and elevation gain are measured from the summit of Argentine Peak. Please note that another way of completing Argentine, Square Top and Wilcox would be from the Naylor Lake road and the Silver Dollar Lake trail. See our write up for Mt. Wilcox to learn more.
From the summit of Argentine Peak, head directly south down the ridge line for a half mile to where the ridge splits. Continue on the ridge that runs SSE, losing about 500 feet in elevation to the saddle. Continue SSE and begin ascending on the ridge line toward Square Top. Now you will need to regain nearly 800 feet in elevation to reach the summit. Most of this traverse will be on tundra, embedded rock, and some rubble or scree. The rockiest section will be the last few hundred feet approaching the summit of Square Top, then the summit ridge flattens out as its' name indicates. There are no significant difficulties. The summit of Square Top offers a nice panoramic view of the Mt. Evans massif as well as surrounding terrain. You'll be able to look straight down onto Silver Dollar Lake, Murray Lake and Naylor Lake.
Hiking in this area sometimes affords the opportunity to see some mountain goats. The goats on the Front range are much more accustomed to seeing humans and do not necessarily flee upon approach. When we did this hike with our children in 1989, we encountered a group of about 20 goats, mostly females and their less than a year old kids and perhaps some approaching their second year. Among those were some young males. It was interesting to observe their behavior as we walked right through their midst on the ridge. They had no intention of leaving that ridge for our sake, so we simply walked right through the group. One of the two year old males decided to challenge us. He would stomp and paw at the ground and wag his head back and forth, and even take a few steps toward us as a challenge, but would back off his threat if we simply spread our arms out and yelled at him a little. Twice he challenged us but each time backed away if we just held steady on our course and not let him intimidate us. Now would we try the same approach with a full grown male? No sir, and you should probably not either.
For the return trip, head back down the same ridge you came up and back to the saddle at 13,000 ft., west of Silver Dollar Lake. From the saddle, contour north and thread a route between the two unnamed ponds above Murray Lake, staying as best you can at near the same elevation. Continue to contour until you reach the east-west ridge that connects Argentine and WIlcox. At this point, make a decision as to whether or not to include Wilcox. If you do it will add another 1.8 miles to your day and an additional 550 feet of elevation gain. When finished with Wilcox, return to the same place as where you intersected the connecting ridge. Look north into the Leavenworth valley below and identify the old roadbed that ends near one of the power line structures at about 12,260 ft. On the ridge where you stand, there is a power line support structure. Just a little east of that structure is a trail that drops down north through the steep valley headwall. Coordinates for the trail are: N 39° 36' 39.34" W 105° 46' 05.35". Drop on down that trail for 300 feet, then head out on the tundra toward the next power line structure. From that structure, head downhill more in the direction of the next structure, but before arriving at it, watch for an opportunity to skirt below some rocky outcrops and above some willows to intersect the old roadbed you observed from up on the ridge. Once on the road, follow it all the way back to the Waldorf Mine where you parked (or the small pond above). The advantage of this route is you can avoid any entanglement with the willows that choke the lower Leavenworth valley.
Links to other information, routes & trip reports for this peak that may be helpful.