Given a complex, separable Hilbert space H, we consider differential expressions of the type τ = −(d ² /dx ² )I _H + V(x), with x ∈ (x ₀ ,∞) for some x ₀ ∈ ℝ, or x ∈ ℝ (assuming the limit-point property of τ at ±∞). Here V denotes a bounded operator-valued potential V(·) ∈ B(H) such that V(·) is weakly measurable, the operator norm ||V(⋅)||B(H) is locally integrable, and V(x) = V(x)* a.e. on x ∈ [x ₀ ,∞) or x ∈ ℝ. We focus on two major cases. First, on m-function theory for self-adjoint half-line L ² -realizations H _+,α in L ² ((x ₀ ,∞); dx;H) (with x ₀ a regular endpoint for τ, associated with the self-adjoint boundary condition sin(α)u′(x ₀ ) + cos(α)u(x ₀ ) = 0, indexed by the selfadjoint operator α = α* ∈ B(H)), and second, on m-function theory for self-adjoint full-line L ² -realizations H of τ in L ² (ℝ; dx;H). In a nutshell, a Donoghue-type m-function MA,NiDo(⋅) associated with self-adjoint extensions A of a closed, symmetric operator A˙ in H with deficiency spaces N _z = ker (A˙ * −zIH) and corresponding orthogonal projections PNz onto N _z is given by MA,NiDo(z)=PNi(zA+IH)(A)−zIH)−1PNi|Ni;=zINi+(z2+1)PNi(A−zIH)−1PNi|Ni,z∈C∖R. In the concrete case of half-line and full-line Schrödinger operators, the role of A˙ is played by a suitably defined minimal Schrödinger operator H _+,min in L ² ((x ₀ ,∞); dx;H) and H _min in L ² (ℝ; dx;H), both of which will be proven to be completely non-self-adjoint. The latter property is used to prove that if H _+,α in L ² ((x ₀ ,∞); dx;H), respectively, H in L ² (ℝ; dx;H), are self-adjoint extensions of H _+,min , respectively, H _min , then the corresponding operator-valued measures in the Herglotz–Nevanlinna representations of the Donoghue-type m-functions MH+,αDo,N+,i(⋅) and MH,NiDo(⋅) encode the entire spectral information of H _+,α , respectively, H.