We present recent and ongoing work that uses precision frequency generation and phase measurement to test the constancy of the speed of light Local Position Invariance (LPI) and the Lorentz Invariance (LI) of the photon with respect to the Standard Model of Particle Physics under the frame work of the Standard Model Extension (SME). The first experiment consists of a pair of orthogonally orientated single crystal sapphire resonators cooled to cryogenic temperatures and configured as stable oscillators operating in Whispering Gallery Mode (Cryogenic Sapphire Oscillator). The experiment is continuously rotated at a period of about 20 seconds, and modulations are searched for with respect to an absolute frame of reference. Our experiment has confirmed Lorentz Invariance at sensitivity better than one order of magnitude than previous tests. The experiment is now being upgraded and has the potential to improve this result by further one and a half orders of magnitude. The second experiment consists of a Mach-Zender Interferometer with a magnetic material in one arm. This experiment allows us to measure odd parity and scalar Lorentz violating parameters predicted in the SME, in which the cavity experiment either exhibit suppressed or no sensitivity to. The experiment has been in continuous operation since September 2007 and has put a limit of order 10^-7 on the scalar Lorentz violating parameter, we show that an upgraded experiment can improve this result by a few more orders of magnitude. The final experiment measures over seven years the frequency comparison of a Cryogenic Sapphire Oscillator and a Hydrogen maser at the Paris Observatory. Amongst the data we search for signals correlated with the changing gravitational potential (test of LPI) and reference frame velocity (test of LI), with first results to be presented.