By exploiting the reciprocal theorem of Stokes flow, we find an explicit expression for the first order slip length correction, for small protrusion angles, and for transverse shear over a periodic array of curved menisci. The result is the transverse flow analogue of the longitudinal flow result of Sbragaglia and Prosperetti [“A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces,” Phys. Fluids 19, 043603 (2007)]. For small protrusion angles, it also generalizes the dilute-limit result of Davis and Lauga [“Geometric transition in friction for flow over a bubble mattress,” Phys. Fluids 21, 011701 (2009)] to arbitrary no-shear fractions. While the leading order slip lengths for transverse and longitudinal flow over flat no-shear slots are well-known to differ by a factor of 2, the first order slip length corrections for weakly protruding menisci in each flow are found to be identical.