In the article, we find new dilatation results on non-commutative \(L^p\) spaces. We prove that any self-adjoint, unital, positive measurable Schur multiplier on some \(B(L^2(\Sigma ))\) admits, for all \(1\leqslant p<\infty \), an invertible isometric dilation on some non-commutative \(L^p\)-space. We obtain a similar result for self-adjoint, unital, completely positive Fourier multiplier on VN(G), when G is a unimodular locally compact group. Furthermore, we establish multivariable versions of these results.