We report a deep search for redshifted H i 21cm emission from three damped and sub-damped Lyman- \alpha absorbers ( DLAs ) at z \approx 0.1 with the Green Bank Telescope ( GBT ) . No evidence for a redshifted H i 21cm emission signal was obtained in the GBT spectra of two absorbers , with the data on the third rendered unusable by terrestrial interference . The non-detections of H i 21cm emission yield strong constraints on the H i masses of the associated galaxies , M _ { HI } < 2.3 \times 10 ^ { 9 } \times ( \Delta V / 100 ) ^ { 1 / 2 } M _ { \odot } for the sub-DLA at z = 0.0830 towards J1553+3548 , and M _ { HI } < 2.7 \times 10 ^ { 9 } \times ( \Delta V / 100 ) ^ { 1 / 2 } M _ { \odot } for the DLA at z = 0.0963 towards J1619+3342 , where \Delta V is the H i 21cm line width , in km s ^ { -1 } . This continues the trend of low H i masses found in all low- z DLAs and sub-DLAs that have been searched for redshifted H i 21cm emission . Low-redshift absorbers with relatively low H i column densities , \lesssim few \times 10 ^ { 20 } cm ^ { -2 } , thus do not typically arise in massive gas-rich galaxies .