  We study the interaction between unitary $\rho$-dilations of a pair of
Hilbert space operators and Birkhoff-James orthogonality. We prove that for two
orthogonal operators $T,A$ if $\|T\|=\rho$, then $U_T \perp_B U_A$ for any
unitary $\rho$-dilations $U_T$ of $T$ and $U_A$ of $A$ acting on a common
space. We characterize $\varepsilon$-approximate Birkhoff-James orthogonality
for complex Hilbert space operators. Then find a sharp bound on $\varepsilon$
such that $T \perp_B A$ implies that $U_T \perp_B^{\varepsilon} U_A$ for any
unitary $\rho$-dilations $U_T, U_A$ of $T$ and $A$ respectively. The
Sch\"{a}ffer unitary dilations of a pair of contractions $T,A$ are not
orthogonal in general. We construct Sch\"{a}ffer-type unitary dilations for
contractions which are pairwise orthogonal.
