Spontaneous rhythmic phenomena in nature are often modeled as limit-cycle oscillators, such as the Brusselator for the Belousov–Zhabotinsky reaction and the FitzHugh–Nagumo model for neuronal dynamics. Under suitable conditions, these models can be reduced to phase models that capture the system’s dynamics solely through one-dimensional phase evolution. In this study, we investigate invariants (constants of motion) of several phase models—including the Theta model, the Kuramoto model, and higher-order coupled Kuramoto models—from the perspective of Koopman and Perron–Frobenius operators.