We present methods for built-in test and calibration of phased arrays using code-modulated embedded test (CoMET). Our approach employs Cartesian modulation of test signals within each element using existing phase shifters, combining of these signals into an aggregate code-multiplexed response, downconversion and creation of code-modulated element-to-element "interference products" using a built-in power detector, demodulation of correlations from the digitized interference response, and extraction of amplitude and phase per element using an equation solver. Rotated-axis methodology is discussed for accurate extraction of phase near the original 0/90/180/270 degree axes. Our techniques are demonstrated at board level for both receive and transmit modes using an eight-element 8-16 GHz phased array constructed using ADAR1000 chips from ADI. At 6 GHz, CoMET-extracted gain and phase are accurate to within 0.2 dB and 3 degree compared to network-analyzer measurements. We then employ CoMET in a calibration loop to determinate optimum control settings at 6 GHz, outside the 8-16 GHz band for which the array was designed. We achieve seven-bit phase resolution with equalized gain. The root-mean squared gain and phase errors are improved from 0.8 dB and 8 degree before calibration to 0.1 dB and 1.7 degree after calibration.