In this paper it is envisaged that cognitive radios (CRs) consult a supporting network infrastructure for permission to transmit. The network server either grants or rejects these requests by estimating, from the CRs geo-location and antenna features, the likely impact its transmission would have on incumbents and other CR devices. This decision would be based on a real-time radio environment map [1] which would be kept up to date with readings from CRs, sensors and dynamic radio propagation prediction. By this means coexistence with incumbents and other CRs can be satisfied. It is maintained here that integral-equation (IE)-based algorithms are suitable candidates for the propagation engine given their 'automatic' nature and that they can be implemented to give results arbitrarily close to the exact numerical solution. IE methods based on the Fast Multipole Method are examined as a likely route to achieve the accuracy and speed necessary for real-time propagation mapping. It is concluded that the results obtained using one of the most recent of these, the Field Extrapolation Method (FEXM) [2], are promising for rural/suburban profiles and could serve to enable coexistence, for example, in IEEE802.22 networks. It is also explained how dynamic propagation prediction can address some fundamental security threats to CR networks.