The motivation of this work is the installation of a monitoring system on a new cable-stayed bridge spanning the Adige River 10 km north of the town of Trento. This is a statically indeterminate structure, having a composite steel-concrete deck of length 260 m overall, supported by 12 stay cables, 6 per deck side. These are full locked steel cables of diameters 116 mm and 128 mm, designed for operational loads varying from 5000 to 8000 kN. The structural redundancy suggests that plastic load redistribution among the cables can be expected in the long term. To monitor such load redistribution, the owner decided to install a monitoring system to measure cable stress; the precision specified was of the order of few MPa. However no cable release or any form of on-site calibration involving tension change was allowed. The solution found was a combination of built-on-site electromagnetic and fiber-optic elongation gauges, these appropriately distributed on both the cables and the anchorages. We discuss how the set of gauges allows tension and elongation measurement with the appropriate precision, and compare the initial monitoring results with the tension estimates made using a non-destructive vibration test.