Antibiotic resistance is becoming increasingly problematic for the treatment of infectious disease in both humans and livestock. The bacterium Pseudomonas aeruginosa is often found to be resistant to multiple antibiotics and causes high patient mortality in hospitals. Bacteriophages represent a potential option to combat pathogenic bacteria through their application in phage therapy. Here, we capitalize on previous studies showing how evolution may increase phage infection capacity relative to ancestral genotypes. We passaged four different phage isolates (podoviridae, myoviridae) through six serial transfers on the ancestral strain of Pseudomonas aeruginosa PAO1. We first demonstrate that repeated serial passage on ancestral bacteria increases infection capacity of bacteriophage on ancestral hosts and on those evolved for one transfer. This result is confirmed when examining the ability of evolved phage to reduce ancestral host population sizes. Second, through interaction with a single bacteriophage for 24 h, P. aeruginosa can evolve resistance to the ancestor of that bacteriophage; this also provides these evolved bacteria with cross-resistance to the other three bacteriophages. We discuss how the evolutionary training of phages could be employed as effective means of combatting bacterial infections or disinfecting surfaces in hospital settings, with reduced risk of bacterial resistance compared with conventional methods.