Planetary rotation rate and orbital eccentricity strongly influence planetary climate, but rotation rate is difficult to constrain from observations. This is especially true for slowly rotating planets on highly eccentric orbits, because variations in observed radiative emission caused by rotation and planet-star distance changes can have similar time scales. Here we examine how observed emission might be used to infer rotation rates in such circumstances. We employ an Earth climate model with no land and a slab ocean, and consider two eccentricities (e=0.3 and 0.6) and two rotation rates: an Earth-like period of 24 hours and a pseudo-synchronous period that generalizes spin synchronization for eccentric orbits. We adopt bandpasses of the Mid-Infrared Instrument for the James Webb Space Telescope as a template for future photometry. At e=0.3 the rotation rates can be distinguished if the planet transits near periastron, because pseudo-synchronous rotation produces a strong day-night contrast and thus an emission minimum on the observed periastron night side. However, light curves for fast and slow rotators behave similarly if the planet is eclipsed near periastron; light curves are also similar for either viewing geometry at e=0.6. Rotation rates can nevertheless be distinguished using ratios of emission in different bands, one in the water vapor window with another in a region of strong water absorption. These ratios vary over an orbit by < 0.1 dex for Earth-like rotation, but by 0.3–0.5 dex for pseudo-synchronous rotation because of large day-night contrast in upper-tropospheric water. For planets with condensible atmospheric constituents in highly eccentric orbits, rotation regimes might thus be distinguished with infrared emission observations for a range of viewing geometries.