The North Ridge of Mount Neva scores a covetted *Classic* in Gerry Roach's Indian Peaks Guidebook. It is shorter but harder than the similar nearby Arapaho South Ridge traverse.
Neva's North Ridge can be climbed from either east or west. From the east, start at the 4th of July Trailhead and hike up an easy 3.5 miles past the 4th of July Mine to Arapaho Pass and/or Lake Dorothy. From here, you can see the route plainly. Scramble up the slope above the lake to attain the grassy ridge. From the west, start from the Meadow Creek TH and follow the trail for Caribou Pass and ascend the moderate slopes to the divide.
Having attained the ridge, head south. The going starts out easily enough but gets harder quickly. Downclimb into a couple of clefts by whatever way seems best to you (3rd class). The crux appears soon after when you to ascend a 4th-class wall with exciting views 600' down to the snowfields and lake. Concider a belay on this part if you are at all unsure of your strength, the strength of the key hold, or if the route is at all wet/icy!
From the top of the crux, continue up steep ramps on the daunting slopes of Point 12700. Angle west around Point 12700 following a line of small cairns over rubble. The going is easier from here on as you skirt several more minor summits on the west. The ridgeline narrows again and you'll be walking an airy, though easier path. Several snow routes arrive at the ridge from the east at this point. Much loose rock and exposure make traversing to the east of the ridgeline a bad idea. Soon you clear the last of the ridge and ascend the grassy slopes to the summit.
Descent via the North Ridge is harder than the ascent as the crux must be downclimbed. Alternatives are to take the Northwest Ridge or to hike southwest toward Mt. Jasper and descend the first gulley you encounter down to a pair of unnamed lakes in the Neva-Jasper cirque. Beware! While descending into the cirque is attractive and relatively safe/easy, you're looking at a mile or more of bushwhacking through the valley to attain the Arapaho Pass trail. This is much safer than traversing the ridge again, but may take a long time.
Another option is to traverse the SW ridge to Mt. Jasper, ascend this peak and descend its SE ridge back toward the 4th-of-July Trail for a nice tour of two high 12ers in the Indian Peaks.
If you are a confident climber and conditions are good, you'll have no trouble soloing the crux. For the more cautious and if ice is present, a short rope might be a good idea.