Telomeres use distinct mechanisms (not used by arms or centromeres) to mediate cohesion between sister chromatids. However, the motivation for a specialized mechanism at telomeres is not well understood. Here we show, using fluorescence in situ hybridization and live-cell imaging, that persistent sister chromatid cohesion at telomeres triggers a prolonged anaphase in normal human cells and cancer cells. Excess cohesion at telomeres can be induced by inhibition of tankyrase 1, a poly(ADP-ribose) polymerase that is required for resolution of telomere cohesion, or by overexpression of proteins required to establish telomere cohesion, the shelterin subunit TIN2 and the cohesin subunit SA1. Regardless of the method of induction, excess cohesion at telomeres in mitosis prevents a robust and efficient anaphase. SA1- or TIN2-induced excess cohesion and anaphase delay can be rescued by overexpression of tankyrase 1. Moreover, we show that primary fibroblasts, which accumulate excess telomere cohesion at mitosis naturally during replicative aging, undergo a similar delay in anaphase progression that can also be rescued by overexpression of tankyrase 1. Our study demonstrates that there are opposing forces that regulate telomere cohesion. The observation that cells respond to unresolved telomere cohesion by delaying (but not completely disrupting) anaphase progression suggests a mechanism for tolerating excess cohesion and maintaining telomere integrity. This attempt to deal with telomere damage may be ultimately futile for aging fibroblasts but useful for cancer cells.