Let \(F\) be a set-valued map defined on \([0,T]\times \mathbb{R}^{n}\) and taking values on closed and nonempty subsets of \(\mathbb{R}^{n}\). The authors show that if \(F\) is measurable in \(t\) and Lipschitzian continuous in \(x\), then for a given finite set of trajectories to the problem \[ \dot x(t)\in F(t,x), \quad x(0)=\xi, \tag{1} \] starting from distinct initial points, there exists a continuous selection from the set of solutions to problem (1) that interpolates these trajectories. An argument from the paper of \textit{A. Cellina} and \textit{A. Ornelas} [Rocky Mt. J. Math. 22, 117-124 (1992; Zbl 0752.34012)] is used by the authors. A second result presented in this paper concerns the existence of Lipschitzian selections when \(F\) has compact and convex values.