Continuous-wave (CW) radiation at 148.4 nm is required to drive the ²²⁹Th isomeric transition of a solid-state nuclear clock, and frequency doubling of 296.8-nm light is its most direct source. We generate CW 148.4-nm light by random quasi-phase matching in strontium tetraborate and characterize it with a compact prism spectrometer built for the purpose. The spectrometer separates the harmonic from the pump on a CaF₂ prism, reads the wavelength from the rotation angle of a solar-blind photomultiplier, resolves the two lines with δλ ≈ 0.6 nm, and yields an absolute power calibration. At room temperature the source delivers 1.9 nW at 148.4 nm, rising to 5.7 nW at the optimum crystal temperature. The conversion efficiency is also strongly structured in temperature: between 30 degree and 50 degree it shows several pronounced maxima, with neighbouring extrema only a few degrees apart, so that a small temperature excursion moves the output from a maximum to a minimum. These results provide practical guidance for optimizing and stabilizing 148.4-nm sources for solid-state ²²⁹Th nuclear clocks.