The discovery of graphene, a unique two-dimensional electron system with extraordinary physical properties, has ignited tremendous research activity in both science and technology. Graphene interactions with a substrate such as, for example, SiO₂/Si are known to strongly limit the electrical performance of graphene devices. Suspended graphene devices, where the interaction with substrates can be strongly reduced, have been studied by macroscopic transport measurements and shown to have a 10-fold increase in mobility. However, a detailed investigation of electronic properties of suspended graphene on a microscopic scale is still missing. In this talk we present a scanning tunneling microscopy/spectroscopy (STM/STS) study of free-standing graphene membranes. The device was fabricated from a graphene flake exfoliated over an array of 1 µm holes etched in SiO₂/Si substrate. Electronic spectra of both suspended and supported regions of single-layer graphene can be probed using STM/STS in a perpendicular magnetic field with varying back gate voltages applied to the Si substrate. We found that both the scanning probe tip and applied back gate voltage induce mechanical deformations in the suspended graphene membrane, which, in turn, influences the graphene electronic spectrum. The significant differences found in the electronic spectra of suspended and non-suspended graphene will be discussed.