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It goes back to Ahlfors that a real algebraic curve $C$ admits a separatingmorphism $f$ to the complex projective line if and only if the real part of thecurve disconnects its complex part, i.e. the curve is \textit{separating}. Thedegree of such $f$ is bounded from below by the number $l$ of real connectedcomponents of $ \mathbb{R} C$. The sharpness of this bound is not a prioriclear. We prove that real algebraic separating curves, embedded in some ambientsurface and with $l$ bounded in a certain way, do not admit separatingmorphisms of lowest possible degree. Moreover, this result of non-existence canbe applied to show that certain real separating plane curves of degree $d$, donot admit totally real pencils of curves of degree $k$ such that $kd \leq l$.

Obstructions for the existence of separating morphisms and totally real pencils