We report interferometric observations tuned to the redshifted neutral hydrogen (H i) 21cm emission line in three strongly lensed galaxies at z ∼ 0.4 with the Giant Metrewave Radio Telescope (GMRT). One galaxy spectrum (J1106+5228 at z=0.407) shows evidence of a marginal detection with an integrated signal-to-noise ratio of 3.8, which, if confirmed by follow-up observations, would represent the first strongly lensed and most distant individual galaxy detected in H i emission. Two steps are performed to transcribe the lensed integrated flux measurements into H i mass measurements for all three target galaxies. First, we calculate the H i magnification factor µ by applying general relativistic ray-tracing to a physical model of the source-lens system. The H i magnification generally differs from the optical magnification and depends largely on the intrinsic H i mass M HI due to the H i mass-size relation. Second, we employ a Bayesian formalism to convert the integrated flux, amplified by the M HI -dependent magnification factor µ, into a probability density for M HI , accounting for the asymmetric uncertainty due to the declining HI mass function (Eddington bias). In this way, we determine a value of log 10 (M HI /M ) = 10.2 +0.3 −0.7 for J1106+5228, consistent with the estimate of 9.4 ± 0.3 from the optical properties of this galaxy. The H i mass of the other two sources are consistent with zero within a 95 per cent confidence interval however we still provide upper limits for both sources and a 1σ lower limit for J1250-0135 using the same formalism.