Cables are subject to local impedance faults, or soft faults, e.g., following mechanical alterations. While their occurrence can be detected, no simple procedure exists for assessing whether a fault is critical and requires intervention. Previous work has demonstrated that the amplitude of echoes generated by time-domain reflectometry does not measure how severe such faults are, hindering attempts at introducing early-warning schemes that could prevent these faults from eventually evolving into hard faults, i.e., open or short circuits. This paper introduces a model-based identification procedure that is capable of accurately inferring how severe an impedance modification along a cable is, together with its length. Its has the advantage of operating at lower frequencies than other more complex identification methods, while being intrinsically stable and well-defined since faults are identified and located in separate steps, without requiring non-linear regression techniques. The proposed method is also shown to remove the typical ambiguities found in the interpretation of time-domain reflectometry signals, by reinstating a single reflection peak in reflectograms. General feasibility conditions for the identification of impedance faults are discussed, proving that only sufficiently long faults can univocally be identified. The accuracy of the proposed method is tested against experimental results obtained for faults of increasing severity in coaxial cables, for which time-domain reflectometry is shown to yield accurate estimates only when testing over a bandwidth almost ten times wider.