A cyclic edge-cut of a graph \(G\) is an edge set whose removal separates two cycles. If \(G\) has a cyclic edge-cut, it is said to be cyclically separable. For a cyclically separable graph \(G\), the cyclic edge-connectivity \(c\lambda(G)\) is the cardinality of a minimum cyclic edge-cut of \(G\). Let \(\zeta(G) = \min\{w(X) \mid X \text{ induces a shortest cycle in } G\}\), where \(w(X)\) is the number of edges with one end in \(X\) and the other end in \(V(G) – X\). A cyclically separable graph \(G\) with \(c\lambda(G) = \zeta(G)\) is said to be cyclically optimal. In this work, we discuss the cyclic edge connectivity of regular double-orbit graphs. Furthermore, as a corollary, we obtain a sufficient condition for mixed Cayley graphs, introduced by Chen and Meng \([3]\), to be cyclically optimal.