Added to their high dexterity and ability to conform to complex shapes, continuum robots can be further improved to provide safer interaction with their environment. Indeed, controlling their stiffness is one of the most challenging yet promising research topics. We propose a tubular stiffening sheath as a replaceable cover for small-diameter continuum robots to temporarily increase the stiffness in a certain configuration. In this article, we assess and compare performances of two different stiffening modalities: granular and layer jamming, provide arguments for material selection and experimental results for stiffness with respect to lateral and axial applied forces. Furthermore, we detected empirically additional effects relating sheath stiffness to material parameters and added to recent investigations in the state of the art, which are based exclusively on material roughness. Finally, we integrated the selected layer jamming material in a miniaturized sheath (13 mm outer diameter, 2.5 mm wall thickness) and covered a tendon-actuated continuum robot with it. Experimental characterization of the behavior with respect to applied external forces was performed via stiffness measurements and proved that the initial tendon-actuated continuum robot stiffness can be improved by a factor up to 24.