Although previous studies of today’s globalised and competitive research landscape have mentioned the research collaborations of CANZUK countries (i.e., Australia, Canada, New Zealand, and the United Kingdom), none have yet studied them in detail. Further, such studies have used different measures of international research collaboration (IRC), resulting in disparate findings. This paper, therefore, analyses the strengths of CANZUK research collaborations, how those collaborations have changed over time, and assesses the effect of three ways of measures on the results (absolute strength, bilateral similarity, and multilateral similarity). We provide a detailed characterisation of the CANZUK research network and its relationships with partner countries, which reveals that the most collaborative CANZUK countries are the UK and Australia, among other findings. We also confirm that many findings differ depending on which measures are used. We offer an explanation of this difference with reference to the nature of the measures (i.e., what they really measure) and make suggestions for suitable measures in future studies depending on their purpose. Finally, we discuss how this study’s findings can be used by research policy makers (in CANZUK and elsewhere) in deciding on research strategy and by researchers in appropriately measuring IRC.