It has long been speculated that cellular microdomains are important for many cellular processes, especially those involving Ca2+ signalling. Measurements of cytosolic Ca2+ report maximum concentrations of less than few micromolar, yet several cytosolic enzymes require concentrations of more than 20 microM Ca2+ to be activated. In this paper, we have resolved this apparent paradox by showing that the surface topology of cells represents an important and hitherto unrecognized feature for generating microdomains of high Ca2+ in cells. We show that whereas the standard modeling assumption of a smooth cell surface predicts only moderate localized effects, the more realistic "wrinkled" surface topology predicts that Ca2+ concentrations up to 80 microM can persist within the folds of membranes for significant times. This intra-wrinkle location may account for 5% of the total cell volume. Using different geometries of wrinkles, our simulations show that high Ca2+ microdomains will be generated most effectively by long narrow membrane wrinkles of similar dimensions to those found experimentally. This is a new concept which has not previously been considered, but which has ramifications as the intra-wrinkle location is also a strategic location at which Ca2+ acts as a regulator of the cortical cytoskeleton and plasma membrane expansion.