We have patterned thin film YBa2Cu3O7-delta (YBCO) coplanar resonators to characterise the surface impedance of our films[l]. Our best film, with growth conditions optimised for good dc transport properties, yields a resonator with an unloaded quality factor in excess of 40000 at 15K and 8GHz, with a corresponding surface resistance around 25muOMEGA. The impedance is constant for microwave fields H(rf) up to 10(4)Am-1, above which it increases rapidly. This contrasts with the case of less well optimised films; although the surface resistances of these films may be less than a factor of 2 larger than those for optimised films, the non-linear effects are much more pronounced and occur at much lower microwave fields, and they are therefore less suitable for high field applications.