The thermodynamic properties of a working-fluid pair, composed of a refrigerant and an absorbent, greatly influence the performance of an absorption-refrigeration cycle. Particularly important is the solubility of the vaporized refrigerant in the absorbent. Using an isochoric saturation method, solubilities were measured for trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) in 1-butyl-3-methylimidazolium hexafluorophosphate ([Bmim]-[PF6]), 1-hexyl-3-methylimidazolium hexafluorophosphate ([Hmim][PF6]), and 1-methyl-3-octylimidazolium hexafluorophosphate ([Omim][PF6]) from 283.15 to 343.15 K. Solubilities rise with a decrease in temperature and an increase in pressure. The highest solubility is in [Omim]-[PF6], followed by [Hmim]-[PF6], and [Bmim]-[PF6]. The new data were correlated by the nonrandom two-liquid model and by the Krichevsky-Ilinskays equation; both provide good agreement with the experimental data. Estimates were given for total enthalpy, entropy, and Gibbs energy of dissolution.