In the mammalian suprachiasmatic nucleus (SCN), a population of noisy cell-autonomous oscillators synchronizes to generate robust circadian rhythms at the organism-level. Within these cells two isoforms of Cryptochrome, Cry1 and Cry2, participate in a negative feedback loop driving circadian rhythmicity. Previous work has shown that single, dissociated SCN neurons respond differently to Cry1 and Cry2 knockouts: Cry1 knockouts are arrhythmic while Cry2 knockouts display more regular rhythms. These differences have led to speculation that CRY1 and CRY2 may play different functional roles in the oscillator. To address this proposition, we have developed a new coupled, stochastic model focused on the Period (Per) and Cry feedback loop, and incorporating intercellular coupling via vasoactive intestinal peptide (VIP). Due to the stochastic nature of molecular oscillations, we demonstrate that single-cell Cry1 knockout oscillations display partially rhythmic behavior, and cannot be classified as simply rhythmic or arrhythmic. Our model demonstrates that intrinsic molecular noise and differences in relative abundance, rather than differing functions, are sufficient to explain the range of rhythmicity encountered in Cry knockouts in the SCN. Our results further highlight the essential role of stochastic behavior in understanding and accurately modeling the circadian network and its response to perturbation.