Given reduced amalgamated free products of C$^*$-algebras $(A,\phi)=\freeprodi(A_\iota,\phi_\iota)$ and $(D,\psi)=\freeprodi(D_\iota,\psi_\iota)$, an embedding $A\hookrightarrow D$ is shown to exist assuming there are conditional--expectation--preserving embeddings $A_\iota\hookrightarrow D_\iota$. This result is extended to show the existence of the reduced amalgamated free product of certain classes of unital completely positive maps. Finally, analogues of the above mentioned results are proved for amagamated free products of von Neumann algebras.