Although scientometric and bibliometric studies embrace a much wider perspective of the linkages/networks of R&D institutions than standard economic studies, to the best of our knowledge, these studies have not yet made use of scientometric tools to analyse the influence and impact of R&D institutions. Moreover, the international perspective has so far been neglected both in standard and bibliometric studies. Based on networks of 1239 foreign co-authorships and 13035 foreign citation linkages, we demonstrate that INESC Porto international influence has considerably expanded since 2003, a year that coincided with the implementation of an internal policy of granting monetary prizes to publications in scientific international journals. In terms of co-authorship, the network of INESC Porto more than duplicated (13 countries in the initial period to 27 in 2004-07). In terms of citations, INESC Porto’s network encompassed almost 40 countries during the whole period (1996-2007). Its more prolific units (optoelectronics, energy and multimedia) presented a rather distinct pattern both in terms of size and evolution of the corresponding network boundaries. The network size of foreign co-authorships was not much different between the three units by the beginning of the 2000s (around 10 countries) but it evolved quite distinctly. The most remarkable pattern was registered by the multimedia (UTM) unit, whose network size rose exponentially to 21 countries in 2004-07. This contrasted with the decline (down to 8 countries) of the energy (USE) unit. The citation network of the optoelectronic unit (UOSE) was by far the largest, until 2003, involving 34 distinct countries, which contrasted with the size of USE (12 countries) and UTM (1 country). But again, after 2003, the size of the citation network of USE and UTM converged spectacularly to that of UOSE’s, reaching in the last period 21 and 16, respectively. The influence of INESC Porto reaches all five continents, especially when we consider citation networks. Indeed, excluding the citations from authors affiliated in Portuguese institutions, those that most cite INESC Porto’s (and UOSE’s) works are affiliated in institutions located in China, the UK and the US. The scientific works produced by USE influences mostly authors affiliated in institutions located in India, China and Spain, whereas for UTM the corresponding countries are the US, Germany and Italy. We infer from the evidence analysed that not only did the boundaries of INESC Porto’s scientific network substantially enlarge in the period of analysis (1996-2007) but its ‘quality’ also evidenced a positive evolution, with authors affiliated in institutions located in the scientific frontier countries citing works of INESC Porto (and its units).