This study is focused on resistance to carbapenems and third-generation cephalosporins in Gram-negative microorganisms isolated from swine, whose transmission to humans via pork consumption cannot be excluded. In addition, the common carriage of carbapenem-resistant (CR) bacteria between humans and pigs was evaluated. Sampling involved 300 faecal samples collected from slaughtered pigs and 300 urine samples collected from 187 hospitalised patients in Parma Province (Italy). In swine, MIC testing confirmed resistance to meropenem for isolates of Pseudomonas aeruginosa and Pseudomonas oryzihabitans and resistance to cefotaxime and ceftazidime for Escherichia coli, Ewingella americana, Enterobacter agglomerans, and Citrobacter freundii. For Acinetobacter lwoffii, Aeromonas hydrofila, Burkolderia cepacia, Corynebacterium indologenes, Flavobacterium odoratum, and Stenotrophomonas maltophilia, no EUCAST MIC breakpoints were available. However, ESBL genes (blaCTXM-1, blaCTX-M-2, blaTEM-1, and blaSHV) and AmpC genes (blaCIT, blaACC, and blaEBC) were found in 38 and 16 isolates, respectively. P. aeruginosa was the only CR species shared by pigs (4/300 pigs; 1.3%) and patients (2/187; 1.1%). P. aeruginosa ST938 carrying blaPAO and blaOXA396 was detected in one pig as well as an 83-year-old patient. Although no direct epidemiological link was demonstrable, SNP calling and cgMLST showed a genetic relationship of the isolates (86 SNPs and 661 allele difference), thus suggesting possible circulation of CR bacteria between swine and humans.