EM response profiles and Argand diagrams of the peak profile response have been calculated for the horizontal loop (Slingram) system and a large vertical plate target conductor in a conductive host medium. Five host models, a homogeneous half-space and four two-layer earths, simulate a range of field conditions and survey parameters. As host medium conductivity is increased, the initial effect on the Argand diagram of the Slingram anomaly is a slight counterclockwise phase rotation and anomaly enhancement due to channeling of current from the host medium into the conductor. Further increases lead to strong clockwise phase rotations and greater anomaly enhancement. Clockwise phase rotations continue, but eventually the anomaly becomes attenuated when propagation losses suffered by the fields in transit through the host become more significant. When background values from survey profiles are used to appraise the conductivity layering of the host, appropriate Argand diagrams can be chosen to obtain from anomaly profiles estimates of conductor depth and conductance which are independent of prospecting frequency. Three case histories support this claim, one of which gives good agreement between model and field data over four octaves of frequency.--Modified journal abstract.