Nature has evolved complex enzyme architectures that facilitate the synthesis and manipulation of the biopolymers DNA and RNA, including enzymes capable of attaching to the biopolymer substrate and performing several rounds of catalysis before dissociating. Many of these 'processive' enzymes have a toroidal shape and completely enclose the biopolymer while moving along its chain, as exemplified by the DNA enzymes T4 DNA polymerase holoenzyme and lambda-exonucleoase. The overall architecture of these systems resembles that of rotaxanes, in which a long molecule or polymer is threaded through a macrocycle. Here we describe a rotaxane that mimics the ability of processive enzymes to catalyse multiple rounds of reaction while the polymer substrate stays bound. The catalyst consists of a substrate binding cavity incorporating a manganese(III) porphyrin complex that oxidizes alkenes within the toroid cavity, provided a ligand has been attached to the outer face of the toroid to both activate the porphyrin complex and shield it from being able to oxidize alkenes outside the cavity. We find that when threaded onto a polybutadiene polymer strand, this catalyst epoxidizes the double bonds of the polymer, thereby acting as a simple analogue of the enzyme systems.