(1) Background: Patent foramen ovale (PFO) is a congenital abnormality present in up to 25% of the general population, and it is a relevant cause of cryptogenic stroke. We applied the hospital-based HTA model (AdHopHTA) to conduct a multidimensional assessment of NobleStitch EL, an innovative suture-mediated PFO closure device. We compared it to Amplatzer PFO Occluder (APO) to provide evidence to inform technologies’ governance in hospital settings. (2) Methods: For each AdHopHTA dimension we: systematically retrieved available evidence from the literature applying the PRISMA guidelines and then analyzed original clinical and cost data of a NobleStitch EL device at San Raffaele research hospital in Milan (Italy). The economic dimension was analyzed through activity-based costing and a cost analysis. We conducted semi-structured interviews with selected healthcare professionals to explore the organizational, legal, social, and ethical impact. (3) Results: A single study was included for the NobleStitch EL, with 10 for APO. Both literature data and original data showed comparable safety. Efficacy data analysis found that the PFO closure was at 89% for NobleStitch EL vs. 89–97% for APO. APO has a better impact on the budget and minor process costs. Consulted experts reported that the organizational impact of NobleStitch EL in the short and the long run as null, albeit a better impact under the social and the ethical aspects. (4) Conclusion: We suggest that there is inadequate evidence to conclude the relative efficacy of NobleStitch EL as compared to APO. Nevertheless, this report shows a good safety profile and higher costs for NobleStitch EL, with no organizational or legal impact. Further studies in selected population are recommended.