Passive vibration control using blocks of viscoelastic materials with macro- and microscopic inclusions has been widely investigated. Significant changes in the vibration response have been observed with such inclusions. We have found that their response changes much more significantly if thin microstructures and channels are carved within these materials and are filled with a high-viscosity fluid. In this paper, we report the passive response of a replicated array of oil-filled microchannels, structured within a block made up of polydimethylsiloxane. Constrained and unconstrained vibration-damping experiments are performed on this block, wherein its vibration suppression ability is detected by applying an excitation signal transversely at the geometric center of the lower face of the block. We observe an increase in the fundamental frequency due to change in stiffness of the block and an increase in damping ratio and loss factor owing to the development of a slip boundary condition between the oil and the microchannel walls causing frictional dissipation of the coupled energy. All vibration experiments have been performed using a single-point laser to ascertain the experimental behavior of the system. We have also modeled the vibration suppression characteristics of such systems both analytically and by using simulation tools $hfill$[2011-0273]