In fact, IIRC you cross the Continental Divide at ~3,000 feet, and there is not a mountain nearby!
According to the high and low elevation map on the Union Pacific web site, the high elevation on the Sunset Limited route is 5,078 feet at Paisano, Texas, milepost 619.26. That is, 619.26 miles west of Houston. The show a secon high elevation a few miles west at Etholen, Texas, 4,653 feet at milepost 741.40. The Sunset Route also gets you below sea level. The low point is -205 feet elevation at Forrum, California, which is at milepost 612.00, zero being at San Francisco. You would be following the edge of the Salton Sea at this location.