We propose in this paper new expressions relating lightning return stroke currents and far radiated electric and magnetic fields, taking into account the presence of an elevated strike object. The derived expressions show that the presence of an elevated strike object enhances the radiated electromagnetic field. The enhancement with respect to a return stroke initiated at ground level is expressed simply through a factor equal to (1+c/v), where v and c are the return stroke speed and the speed of light, respectively. The computed results using the proposed expression are compared with sets of simultaneously-measured currents and fields associated with lightning strikes to the Toronto CN Tower, and a reasonable agreement is found.