EPR resonators on the basis of standing-wave cavities are optimised for large samples. For small samples it is possible to design different resonators that have much better power handling properties and higher sensitivity. Other parameters being equal, the sensitivity of the resonator can be increased by minimising its size and thus increasing the filling factor. Like in NMR, it is possible to use lumped elements; coils can confine the microwave field to volumes that are much smaller than the wavelength. We discuss the design and evaluation of EPR resonators on the basis of planar microcoils. Our test resonators, which operate at a frequency of 14 GHz, have excellent microwave efficiency factors, achieving 24 ns pi/2 EPR pulses with an input power of 17 mW. The sensitivity tests with DPPH samples resulted in the sensitivity value 2.3 x 10(9) spins.G(-1) Hz(-1/2) at 300 K.