Cold-electron bolometers (CEBs) integrated with twin-slot antennas have been designed and fabricated. Optical response was measured at bath temperatures of 0.06 to 3 K using blackbody radiation source at temperatures of 3 to 15 K. The responsivity of 0.3 * 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> V/W was measured at 2.7-K blackbody temperature that is close to the temperature of the cosmic microwave background. Optical measurements indicate quasi-optical coupling efficiency of up to 60% at low phonon temperature and low signal level. Estimations for bolometer responsivity were made for practical range of bath temperatures and blackbody radiation temperatures. The estimated ultimate dark responsivity at 100-mK bath temperature can approach S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</sub> = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> V/W and reduces down to 1.1 * 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> V/W at 300 mK for a device with absorber volume of 5 * 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-20</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> .