A percussion drilling assembly includes a housing with a hammer bit disposed in the lower end portion thereof and configured to move longitudinally within the housing. The hammer bit includes an annular bit shank having a bit strike face and a cutting structure at a lower end portion thereof. An annular piston having a piston strike face arranged and designed to strike the bit strike face is also disposed in the housing. At least one of the bit strike face and the piston strike face has a toroidal curvature profile. A method includes one or more of lowering the percussion drilling assembly into a borehole, engaging the cutting structure with a formation, and impacting the bit strike face of the annular bit shank with the piston strike face of the annular piston.