Sandwich panels are often used in aerospace structures where high stiffness-to-weight is required, such as aircraft fuselage shells. Interior noise reduction in aircraft using such panels is a challenge because acoustic attenuation is reduced for light, stiff composite structures - especially those manufactured to have fewer mechanical joints. Acoustic metamaterials offer an approach to reducing the dynamic response of, and noise transmission through, sandwich panels. The key concept underlying this approach is to consider a metamaterial as a highly distributed system of tuned vibration absorbers that introduces one or more stop bands in which range the response of the global structure is reduced. The resonance frequency (or frequencies) of the absorber system may be tuned to match an excitation frequency and/or a global resonance frequency. Using the assumed-modes method, an initial metamaterial system was designed for integration into the honeycomb core of a representative sandwich panel; this design was refined using finite element analysis. To determine the dynamic response of the global sandwich panel, the metamaterial system was modeled as an effective distributed complex mass density. The cores for two sandwich panels were fabricated using 3-D printing technology, using a stiff polymer for the baseline honeycomb core, and a combination of a stiff and soft/lossy polymers for the metamaterial-augmented core. The cores were characterized statically to determine effective elastic properties, and dynamically to determine the natural frequencies and loss factors of the metamaterial system. Unidirectional carbon-fiber face sheets were bonded to both cores to construct sandwich panels. The sandwich panels were tested dynamically for two different boundary conditions, cantilevered and free-free. Experimental results confirmed that the metamaterial core reduced the peak dynamic response at the natural frequencies of the sandwich panel - typically by about 10 dB - with reasonably good agreement with model predictions.