We present the design, integration, and first ryogenic testing of our new broad-band millimeter-wave spectrometer, Z-Spec. Z-Spec uses a novel architecture called WaFIRS (Waveguide Far-IR Spectrometer), which employs a curved diffraction grating in a parallel-plate waveguide propagation medium. The instrument will provide a resolving power betwee 200 and 350 across an instantaneous bandwidth of 190-310 GHz, all packaged within a cryostat that is of order 1 meter in size. For background-limited astronomical observations in the 1mm terrestrial window, Z-Spec uses 160 silicon nitride micro-mesh bolometers and the detectors and waveguide grating are cooled to ~0.1 K. Our first cryogenic measurements at 225 GHz show resolving power greater than 200, and the end-to-end throughput is estimated to be greater than 30%, possibly as high as 40%. Z-Spec represents the first systematic approach to cosmological redshift measurement that is not based on optical or near-IR identifications. With its good sensitivity and large bandwidth, Z-Spec provides a new capability for millimeter-wave astrophysics. The instrument will be capable of measureing rotational carbon monoxide line emission from bright dusty galaxies at redshifts of up to 4, and the broad bandwidth insures that at least two lines will be simultaneously detected, providing an unambiguous redshift determination. In addition to Z-Spec's observations over the next 1-3 years, the WaFIRS spectrometer architecture makes an excellent candidate for mid-IR to millimeter-wave spectrometers on future space-borned and suborbital platforms such as SPICA and SAFIR. The concept is dramatically more compact and lightweight than conventional free-space grating spectrometers, and no mirrors or lenses are used in the instrument. After the progress report on Z-Spec we highlight this capability.