An ultra-low-background proportional counter design has been developed at Pacific Northwest National Laboratory (PNNL) using clean materials, primarily electro-chemically-purified copper. This detector, along with an ultra-low-background counting system (ULBCS), was developed to complement a new shallow underground laboratory (30 meters water-equivalent) at PNNL. The ULBCS design includes passive neutron and gamma shielding, along with an active cosmic-veto system. This system provides a capability for making ultra-sensitive measurements to support applications like age-dating soil hydrocarbons with 14C/3H, age-dating of groundwater with 39Ar, and soil-gas assay for 37Ar to support On-Site Inspection (OSI). On-Site Inspection is a key component of the verification regime for the Comprehensive Nuclear-Test-Ban Treaty (CTBT). Measurements of radionuclides created by an underground nuclear explosion are valuable signatures of a Treaty violation. For OSI, the 35-day half-life of 37Ar, produced from neutron interactions with calcium in soil, provides both high specific activity and sufficient time for inspection before decay limits sensitivity. This work describes the calibration techniques and analysis methods developed to enable quantitative measurements of 37Ar samples over a broad range of proportional counter operating pressures. These efforts, along with parallel work in progress on gas chemistry separation, are expected to provide a significant new capability for 37Ar soil gas background studies.