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The electromagnetic radiation from a VLSI chip package and heatsink structure is analyzed by means of the finite-difference-time-domain (FDTD) technique. The dimensions of a typical configuration call for a multizone gridding scheme in the FDTD algorithm to accommodate fine grid cells in the vicinity of the heatsink and package cavity and sparse gridding in the remainder of the computational domain. The issues pertaining to the effects of the heatsink on the overall radiative capacity of the configuration are addressed. Analyses are facilitated by using simplified heatsink models and by using dipole elements as sources of electromagnetic energy to model the VLSI chip. The potential for enhancement of spurious emissions by the heatsink structure is illustrated. For heatsinks of typical dimensions, resonance is possible within the low gigahertz frequency range. The exploitation of the heatsink as an emissions shield by appropriate implementation schemes is discussed and evaluated.