The Underground Nuclear Explosion Signatures Experiment (UNESE) sought to use 37Ar as a tracer for measuring noble-gas migration in the soil surrounding historic Underground Nuclear Explosions (UNE). One unexpected observation was the presence of the much longer-lived isotope 39Ar from historic UNEs. Quantifying the activity of 39Ar proved difficult due to the lack of capability to measure significantly-above-background levels of 39Ar and a general discomfort to repeatedly expose Ultra-Low-Background Proportional Counters (ULBPCs) to significant radioactivity. Because the whole-air samples collected for the 37Ar tracer measurement were already being measured on the above-ground argon capability, it was decided to expand that capability to include 39Ar. This document describes the efforts required to achieve quantitative reporting of the 39Ar backgrounds measured during experiments at the sites of the historic Barnwell and Disko Elm UNEs.