When interacting with a virtual object (VO) through a haptic device, it is crucial to feedback a contact force to the human operator (HO) that displays the VO physical properties with high fidelity. The core challenge, here, is to expand the renderable range of these properties, including larger stiffness and smaller inertia, at the available sampling rate. To address this challenge, a framework entitled high-fidelity contact rendering (HFCR) has been developed in this paper. The framework consists of three main strategies: an energy-based rendering of the contact force, smooth transition (ST) between contact modes, and remaining leak dissipation (LD). The essence of these strategies is to make the VO emulate its continuous-time counterpart. This is achieved via physically meaningful modifications in the constitutive relations to suppress artificial energy leaks. The strategies are first developed for the one-dimensional (1D) canonical VO; then, generalization to the multivariable case is discussed. Renderability has been analyzed exploring different stability criteria within a unified approach. This leads to stability charts and identification of renderable range of properties in the presence and absence of the HO. The framework has been validated through simulation and various experiments. Results verify its promising aspects for various scenarios including sustained contact and sudden collision events with or without the HO.