We report interferometric observations tuned to the redshifted neutral hydrogen (H I) 21cm emission line in three strongly lensed galaxies at z similar to 0.4 with the Giant Metrewave Radio Telescope. 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 mu 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-H I due to the H I mass-size relation. Secondly, we employ a Bayesian formalism to convert the integrated flux, amplified by the M-HI-dependent magnification factor mu, into a probability density for M-H I, accounting for the asymmetric uncertainty due to the declining H I mass function (Eddington bias). In this way, we determine a value of log(10) (M-H I/M-circle dot) = 10.2(-0.7)(+0.3) 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 l sigma lower limit for J1250-0135 using the same formalism.