The retrieval of the cross-sectional contour of a homogeneous, multiply connected cylindrical obstacle located in free space is performed via controlled evolution of a level set from experimental data in either the transverse magnetic (TM) or transverse electric (TE) polarization case as is described in the introductory paper of the special section. Theoretical and algorithmic details on the solution method are found in Ramananjaona et al (2001 Inverse Problems 17 1087–111) for the buried object configuration—the free-space configuration is a straightforward simplification—and only key elements are recalled here. Focus is on the display and discussion of shape identification results for the two dielectric circular cylinders (TM data), the rectangularly shaped metal cylinder (TM and TE data), and the U-shaped metal cylinder (TM data). In addition to the fact that TE data are often seen as more of a challenge that TM data, those cases appear to be the most demanding ones in the microwave data base in terms of geometry (the U-shaped one) or in view of the inversion algorithm itself (developed for penetrable objects, the metal case is in principle off limits) whilst the two cylinders illustrate how multiply connected, dielectric objects are retrieved.