We have simulated and experimentally tested a coaxial probe measuring system to be used in distinguishing between normal (healthy) breast tissue and cancerous (often malignant) breast tissue. The system employs commercially available components including an Agilent 8363B phase network analyzer (PNA) and an Agilent 85070D dielectric probe. Instead of the Agilent software three material calibration technique, we propose a four material calibration method across the frequency range of 3-17 GHz for more robust measurements of the complex permittivity. Experimental results on human and snake tissues show the non-homogeneous nature of biological tissues and also illuminate the dependence of complex permittivity on tissue temperature. Building upon the differences and also the variation seen in complex permittivity in literature between normal and cancerous breast tissue across this frequency range, we propose a technique which utilizes a neural network where multiple measurements are input in making the final decision on whether or not the tissue under test is cancerous. Simulation results using Ansoft HFSS are provided here and show the potential of microwave diagnosis of breast cancer.Index Terms -Open-ended coaxial probe, breast cancer detection, complex permittivity, neural networks.