Methods and apparatus for making directional measurements of earth formations surrounding a borehole. New antenna coil shield designs are utilized to provide selective attenuation of at least one electromagnetic energy field component as the component interacts with the shield. The new shields are implemented in several downhole tool configurations to provide azimuthally focused formation measurements. In effect, the new shield filters interacting electromagnetic energy field components to pass those components corresponding to a magnetic dipole oriented at an angle from the tool axis. The shields thereby alter a coil's envelope of influence to electromagnetic energy. The new shields also form part of a system for making directional measurements while drilling.