We describe the use of a near-field scanning microwave microscope to image the permittivity and tunability of bulk and thin film dielectric samples on a length scale of about 1 μm. The microscope is sensitive to the linear permittivity, as well as to nonlinear dielectric terms, which can be measured as a function of an applied electric field. We introduce a versatile finite element model for the system, which allows quantitative results to be obtained. We demonstrate use of the microscope at 7.2 GHz with a 370 nm thick Ba0.6Sr0.4TiO3 thin film on a LaAlO3 substrate. This technique is nondestructive and has broadband (0.1-50 GHz) capability. The sensitivity of the microscope to changes in permittivity is Δ∈r=2 at ∈r=500, while the nonlinear dielectric tunability sensitivity is Δ∈113=10-3 (kV/cm)-1. © 2000 American Institute of Physics.