We report on measurements of picosecond bunch lengths and the energy-z correlation of the bunch with a high energy electron test beam to the A-line and End Station A (ESA) facilities at SLAC. The bunch length and the energyz correlation of the bunch are measured at the end of the linac using a synchrotron light monitor diagnostic at a high dispersion point in the A-line and a transverse RF deflecting cavity at the end of the linac. Measurements of the bunch length in ESA were made using high frequency diodes (up to 100 GHz) and pyroelectric detectors at a ceramic gap in the beamline. Modelling of the beam's longitudinal phase space through the linac and A-line to ESA is done using the 2-dimensional tracking program LiTrack, and LiTrack simulation results are compared with data. High frequency diode and pyroelectric detectors are planned to be used as part of a bunch length feedback system for the LCLS FEL at SLAC. The LCLS also plans precise bunch length and energy-z correlation measurements using transverse RF deflecting cavities.