This paper presents materials and designs for an ultrathin, stretchable class of device that is capable of lamination onto the surface of the skin, for wireless determination of dielectric and surface strain properties. The sensor exploits LC resonators with capacitive electrodes whose radio frequency characteristics change with variations in skin properties, and is capable of conformal and spontaneous integration with skin due to their skin-like, "epidermal", mechanical properties. Resonance frequencies of the LC resonators can be measured wirelessly through changes in the absorption of electromagnetic energy from a coil connected to an impedance measurement setup and placed in proximity to the epidermal device. Experimental results demonstrate that the device offers a precision of 1.1 (arbitrary unit of a reference commercial hydration meter) for hydration and 1.3% for strain detection, with good stability and low drift. Measurement of simulated lymphedema using an expandable balloon with an attached sensor further demonstrates the potential for using such a sensor in monitoring skin swelling. Finite element simulation of physical deformation and associated changes in electrical properties enable quantitative interpretation of the experimental results. The results may have relevance for wireless evaluation of the skin, for applications ranging from dermatology and cosmetology to health/wellness monitoring (lymphedema, transdermal water loss, edema, and psychological stress).