The new superconductor MgB 2 may prove useful for microwave applications at intermediate temperatures. MgB 2 films with the thickness of 300 -400 nm have surface resistance less than 10 at a frequency ( 2 ) of 8.5 GHz and 7 K, and 1.5 m at 87 GHz and 4.2 K. The critical temperature ( ) of these films is 39 K when they are prepared under optimum conditions. The appears to scale as 2 up to 30 K. After surface ion-milling, a reduction of the and an enhanced resistivity ( ) are observed consistently at 8.5 GHz and 87 GHz along with a reduced at low temperatures. The observed ( ) -relation and the uncorrelated behavior between ( ) and values measured at low temperatures are well explained in terms of the two-gap model, with the observed ( ) -relation attributedto the properties of the large gap, and the at lower temperatures reflecting the properties of the small gap, with an enhanced gap energy due to increased interband scattering. This study suggests that the interband scattering should be enhanced to improve the low temperature microwave properties of MgB 2 films and that the ion-milling process must be performed with great care to preserve the high quality of MgB 2 films.