A rotor blade for a turbine of a gas turbine that includes an airfoil, the airfoil having a leading edge, a trailing edge, an outboard tip, and an inboard end that attaches to a root configured to couple the rotor blade to a rotor disc, wherein the airfoil comprises a cooling configuration that includes elongated cooling channels for receiving and directing a coolant through the airfoil, the rotor blade further comprising: a tip shroud connected to the outboard tip of the airfoil, the tip shroud comprising an outboard surface; and branching passages formed through the tip shroud, each of which elongates between a connection with one of the cooling channels and an outlet port formed on a surface of the tip shroud; wherein the branching passages comprise a canted orientation relative the outboard surface of the tip shroud; wherein the tip shroud comprises an axially and circumferentially extending planar component supported by the airfoil at the outboard tip of the airfoil; wherein each of the branching passages defines a discharge direction, the discharge direction comprising a direction that coolant discharged from the branching passage is aimed; wherein a first discharge angle is defined between the discharge direction and the outboard surface of the tip shroud; wherein the first discharge angle comprises a shallow angle; wherein each of the branching passages comprises an outlet section residing near the outboard surface of the tip shroud and terminating at a corresponding outlet port; wherein the discharge direction of each of the branching passages is defined via a continuation from the outlet port of a central axis of the outlet section; wherein the first discharge angle of each of the branching passages comprises a range of between about 10° and 60°; wherein a rotation direction comprises a direction of rotation for the rotor blade during expected operation in the turbine; wherein a second discharge angle is defined between the discharge direction and a reference line parallel to the rotation direction; and wherein the second discharge angle comprises an angle less than about 20°. a tip shroud connected to the outboard tip of the airfoil, the tip shroud comprising an outboard surface; and branching passages formed through the tip shroud, each of which elongates between a connection with one of the cooling channels and an outlet port formed on a surface of the tip shroud; wherein the branching passages comprise a canted orientation relative the outboard surface of the tip shroud; wherein the tip shroud comprises an axially and circumferentially extending planar component supported by the airfoil at the outboard tip of the airfoil; wherein each of the branching passages defines a discharge direction, the discharge direction comprising a direction that coolant discharged from the branching passage is aimed; wherein a first discharge angle is defined between the discharge direction and the outboard surface of the tip shroud; wherein the first discharge angle comprises a shallow angle; wherein each of the branching passages comprises an outlet section residing near the outboard surface of the tip shroud and terminating at a corresponding outlet port; wherein the discharge direction of each of the branching passages is defined via a continuation from the outlet port of a central axis of the outlet section; wherein the first discharge angle of each of the branching passages comprises a range of between about 10° and 60°; wherein a rotation direction comprises a direction of rotation for the rotor blade during expected operation in the turbine; wherein a second discharge angle is defined between the discharge direction and a reference line parallel to the rotation direction; and wherein the second discharge angle comprises an angle less than about 20°.