A transition-to-turbine seal (320) including an upstream portion (322) adapted to engage a flange (416) of a transition (400). The upstream portion (322) may be U-shaped in cross-sectional profile and include a primary wall (324) that includes a proximal section (325) and a distal section (326) relative to a hot gas path (170). The proximal section (325) includes a plurality of recesses (327) which are spaced apart and separated by intervening wall (328). In each recess (327) is provided one or more outlets (329) of cooling fluid holes (339). The outlets (329) communicate via the cooling fluid holes (339) with a supply of compressed cooling fluid, such as compressed air that is provided from the compressor. During operation the outlets (329) release this fluid into the respective recesses (327). The flow of cooling fluid provides for a more uniform cooling effect that includes impingement and convective cooling.