The optimal design of the high temperature superconducting coils of a micro
-SMES is described. Two formulations of die problem are considered which mi
nimize the overall dimensions of the device or the volume of the supercondu
cting coils. Out of the device the stray field is lower than the desired va
lue. The coils are solenoids which can be arranged in an axial symmetric or
toroidal configuration. The results in correspondence to different values
of the stored energy and other parameters of the design are reported and di
scussed.