The spectral performance of freestanding resonant metal-mesh bandpass filters operating with center frequencies ranging from 585 GHz to 2.1 THz is presented. These filters are made up of a 12-μm-thick copper film with an array of cross-shaped apertures that fill a circular area with a 50-mm diameter. The filters exhibit power transmission in the range 97-100% at their respective center frequencies and stop-band rejection in excess of 18 dB. The theoretically predicted nondiffracting properties of the meshes are experimentally verified through high-resolution beam mapping. Scalability of the filter spectra with mesh dimensions is demonstrated over a wide spectral range. Several modeling methods are considered, and results from the models are shown.