We describe the optical characterisation of two silicon cold-electron bolometers each consisting of a small ( $$32\,\times \,14~\mathrm {\upmu m}$$ ) island of degenerately doped silicon with superconducting aluminium contacts. Radiation is coupled into the silicon absorber with a twin-slot antenna designed to couple to 160-GHz radiation through a silicon lens. The first device has a highly doped silicon absorber, the second has a highly doped strained-silicon absorber. Using a novel method of cross-correlating the outputs from two parallel amplifiers, we measure noise-equivalent powers of $$3.0 \times 10^{-16}$$ and $$6.6 \times 10^{-17}~\mathrm {W\,Hz^{{-1}/{2}}}$$ for the control and strained device, respectively, when observing radiation from a 77-K source. In the case of the strained device, the noise-equivalent power is limited by the photon noise. [ABSTRACT FROM AUTHOR]