This study is devoted to find Chen and Chen-Ricci -type inequalities for semi-slant \(\xi ^\perp \) -Riemannian submersions from Sasakian space forms onto Riemannian manifolds. These inequalities reveal relationships between intrinsic invariants, such as Ricci and scalar curvature, and extrinsic invariants like the second fundamental form. Finally, we analyze the conditions under which equality is attained, and we present illustrative examples.