The present invention relates to substrates comprising covalently attached antimicrobial polymers, which act as synthetic mimics of antimicrobial peptides (SMAMPs) and are preferably obtained by ring opening metathesis polymerization (ROMP). The inventive antimicrobial polymers exhibit a molecular weight of more than 100,000 g mol-1 and are preferably covalently attached to the surface of a substrate, e.g. an implant, a medical device, medical equipment or a (tissue- supporting) biomaterial, etc. Covalent bonding may be carried out using a photoreactive crosslinker but also by 'grafting onto' or 'grafting from'. The present invention is also directed to uses of the inventive antimicrobial polymers as defined herein, e.g. for antimicrobially coating a surface of such a substrate with a layer of the inventive antimicrobial polymer.