The efficiency of micro-cell aluminium honeycombs in augmenting heat transfer in compact heat exchangers is evaluated using analytical models. For convective cooling, the overall heat transfer rate is found to be elevated by about two order of magnitudes when an open channel is designed with an aluminium honeycomb core. The performance is comparable to that achieved by using open-celled aluminium foams, but attributed to different mechanisms. At low Reynolds numbers (< 2000), the flow is essentially laminar in honeycombs, in contrast to the largely turbulent flow in metal foams; this deficiency in fluid dynamics is compensated for by the superior surface area density offered by honeycombs over foams. Another advantage of designing heat sinks with honeycombs is the relatively small pressure drop experienced and minimal noise generated by the laminar flow. The overall heat transfer rate of the heat sink is maximised when the cell morphology of the honeycomb is optimised. However, the optimal cell morphology is not constant but dependent upon the geometry and heat transfer condition of the heat sink as well as the type of convective cooling medium used. For air cooling, the optimal relative density of the honeycomb is about 0.1. Other related effects, such as cell orientation and double cell wall thickness, are discussed.