A remarkably strong dependence of magnetoimpedance (MI) on tensile stress has been observed in the microwave frequency range for thin CoMnSiB glass-coated microwires exposed to a special thermal treatment. The MI ratio runs into more than 100% at 0.5-1.5 GHz when the tensile stress of 600 MPa is applied to the wire. It was demonstrated that a large MI change at such high frequencies is related predominantly with the dc magnetization orientation. A host of such microwires incorporated into a dielectric matrix may constitute a new sensing medium that is characterized by the stress-dependent effective permittivity. Such medium can be used for the microwave visualization of the stress distribution inside of a composite structure or on its surface.