A set of amorphous poly[ethylene‐co‐(1,4‐cyclohexanedimethylene terephthalate)] (PECT) copolymers containing 25 and 30% of 1,4‐cyclohexane dimethylene (CHDM) units and small amounts of branching agent pentaerythritol (PER) is investigated. The level of long chain branching was estimated by analyzing the positive deviation from $\eta _0 \sim\overline M _{\rm w}^{3.54}$ law. Branching also produced melt elasticity enhancement which is desirable for certain processing methods. Capillary extrusion experiments at 180 °C generated flow‐induced crystallization in PECT containing 25% of CHDM. Crystallization increased with the amount of PER added, which was explained by the favorable effect of branching to increase elongational rate at the entrance of the capillary. Linear and branched PECTs containing 30% of CHDM did not crystallize.