This paper presents diffraction measurements, analysis, and signal strength prediction models around objects such as corners, pillars, and irregular objects, at 10, 20, and 26 GHz. The diffraction measurements were conducted indoors and outdoors by using a continuous wave (CW) channel sounder with three pairs of identical directional horn antennas at the transmitter and receiver. The measurement results are compared with theoretical predictions based on the Knife Edge Diffraction (KED) in order to determine how well the theoretical model compares to real-world measurements. The KED model is shown to work well for indoor environments, and an empirical linear model with a fixed reference point is also presented and provides a better fit to the measured data around rounded corners in the outdoor environment. Diffraction loss is shown to increase with frequency in outdoor scenarios, but less so inside buildings due to reflection and transmission between walls. The model validation and new models will be useful for designing and calibrating ray-tracers and other wireless network simulators by simulating potential channel loss from diffraction around objects and understanding the impact of diffraction at centimeter-wave and millimeter-wave frequencies in indoor and outdoor environments.