Given operators X and Y acting on a separable Hilbert space $mathcal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate self-adjoint interpolation problems for operators in a tridiagonal algebra : Let $mathcal{L}$ be a subspace lattice acting on a separable complex Hilbert space $mathcal{H}$ and let X = ($x_{ij}$) and Y = ($y_{ij}$) be operators acting on $mathcal{H}$. Then the following are equivalent: (1) There exists a self-adjoint operator A = ($a_{ij}$) in $Alg{mathcal{L}}$ such that AX = Y. (2) There is a bounded real sequence {${alpha}_n$} such that $y_{ij}={alpha}_ix_{ij}$ for $i,j{in}mathbb{N}$.