Woven Nomex (R) ribbon cables made up with superconducting niobium-titanium wire are used at millikelvin temperatures in many large cryogenic instruments. It is important to know how much heat in transmitted down such cables. However, the conductivity of the materials used is not well known. Another problem is that the wires are normally clad with alloys which exhibit some magnetism. This is a potential problem for instruments employing superconducting detectors. A safe non-magnetic alternative to the usual materials is phosphor-bronze clad niobium-titanium wiring. However, there is little experience with such wires. We have therefore measured the conductance of a ribbon cable made up with these wires. The measured values are in good agreement with our predictions, suggesting that the values we have used to model the cable are sufficiently accurate, and could therefore be used to predict the performance of ribbon cables using other cladding materials, so long as the conductivity of the cladding is reasonably well known. As part of our analysis, we consider the likely variation in thermal conductivity values for C51000 phosphor bronze caused by legitimate variations in composition. (C) 2010 Elsevier Ltd. All rights reserved.