A sustained release antimicrobial cannula or catheter for residence within a portion of a human body through which aqueous biological fluids can pass and including a tube. The tube has a polymeric matrix and an antimicrobial agent residing within at least a portion of the polymeric matrix. The polymeric matrix includes cured silicon rubber and the antimicrobial agent is a finely divided nitrofuran compound, a paraben antifungal, or combinations thereof. The antimicrobial agent can diffuse out of the polymeric matrix and into an aqueous biological environment when the polymeric matrix comes into contact with such an aqueous biological environment. Methods of making a sustained release antimicrobial cannula and of catheterizing a patient are also disclosed.