Maturity at harvest is an important determinant of fruit quality in kiwiberry [Actinidia arguta (Siebold & Zucc.) Planch. ex Miq.], a climacteric fruit that is harvested after reaching physiological maturity but not yet ready-to-eat ripeness. Although a recommended cultivar for commercial kiwiberry producers in the northeastern United States is ‘Geneva 3’, no published research exists regarding recommended harvest and postharvest practices for this variety. In this study, conducted across two seasons, ‘Geneva 3’ kiwiberries were harvested at a range of mean maturities (6.5, 8.0, and 10.0°Brix), held in cold storage for various durations (4, 6, and 8 weeks), and then ripened at room temperature. At regular time points during ripening (0, 3, 6, 9, and 12 days), visual quality was assessed, and measurements were taken of soluble solids content, dry matter content, and firmness as a means of characterizing fruit quality. Results show that berries harvested at 6.5°Brix largely became visually unacceptable under cold storage conditions and resulted in lower overall quality fruit. Harvesting at 8.0°Brix resulted in high-quality fruit amenable to cold storage, and such quality was not enhanced by delaying harvest to 10.0°Brix. Fruit harvested at 8.0°Brix after 4 weeks in cold storage was found to be acceptable for consumption for, on average, a 3-day window after ripening at room temperature for 4 days. After 6 weeks in cold storage, the consumability window shortened to ∼2 days, starting after 3 days of ripening at room temperature. After 8 weeks in cold storage, the fruit were found to be largely visually unacceptable for fresh eating. In summary, the results indicate that harvesting ‘Geneva 3’ kiwiberries at 8.0°Brix produces berries with the greatest storability (at least 6 weeks in cold storage), the longest window of peak consumability, and the highest overall quality, while mitigating the risks associated with leaving physiologically mature fruit to ripen further in the field.