The β-delayed proton and γ-ray emission of 37Ca and 36Ca was studied at the projectile fragment separator at GSI Darmstadt. In the 37Ca study, the β-delayed γ decay was observed for the first time, and the half-life was redetermined, under essentially background-free conditions, as 181.1 ± 1.0 ms. The surprisingly high Γ γ Γ p values found for proton-unbound states in 37K drastically reduce former discrepancies between the Gamow-Teller strength values B(GT) measured in the 37Ca β decay and those deduced from the 37Cl(p,n) 37Ar mirror reaction. Our data provide evidence, on a level of 1.6 standard deviations, for isospin-mixing of the lowest T = 3 2 level in 37K. In the 36Ca study, a complete β decay scheme, including the β-delayed proton emission into the ground and first excited states of 35Ar as well as the β-delayed γ decay, was measured for the first time. The 36Ca half-life was remeasured with improved accuracy to be 102 ± 2 ms. Our data exclude a 1 + assignment for two near-thrd states in 36K that could be important resonances in 35Ar(p,γ) reactions of astrophysical interest. The B(GT) distributions in 37,36Ca decays are compared to results obtained from large-scale sd shell-model calculations.