Endovascular procedures involve intricate manoeuvring of medical devices inside arteries, resulting in multiple device-tissue interactions between the devices and the arterial wall, such as tissue deformation and tissue damage. To get more insight into these device-tissue interactions and to enable real-time navigation during a medical procedure, a digital twin is created using model order reduction (MOR) as a digital twin should ideally have a (near) real-time simulation capability. MOR is a technique to reduce the computational complexity by replacing a complex model, called the full order model (FOM), by a model with lower complexity, called the reduced order model (ROM). As a first step to create such a complex digital twin, a ROM of a simple indentation test is created, using the penalty method to model the contact mechanics. Furthermore, a comparison between this method and other methods, such as the Lagrange multiplier method, will be performed to determine the best approach to model contact mechanics. The next step in creating a (near) real-time digital twin, is to introduce a hyper-reduction (HR) technique. This is an additional reduction step to further reduce the computational complexity and consequently the computational time, while ensuring sufficiently accurate results. Since there are multiple HR techniques, this research will also include a comparison of different HR techniques, both theoretically and numerically. Future work includes expanding to more realistic and complex models of device-tissue interactions, for example, maneuvering of a guidewire through an artery, as well as eventually creating a digital twin of those interactions.