This paper proposes optical carrier microwave interferometry (OCMI)-based optical fiber interferometers for sensing applications with improved measurement sensitivity with the assistance of the Vernier effect. Fabry-Perot interferometers (FPIs) are employed in the proof of concept. A single-FPI-OCMI system is first demonstrated for measurements of variations of temperatures by tracking the spectral shift of the interferogram in microwave domain. By cascading two FPIs with slightly different optical lengths, the Vernier effect is generated in the magnitude spectrum of the system with a typical amplitude-modulated signal. By tracking the shift of the envelope signal, temperature measurements are experimentally demonstrated with greatly enhanced sensitivity. The amplification factor for the measurement sensitivity can be easily adjusted by varying the length ratio of the two cascaded FPIs. In addition to the experimental demonstration, a complete mathematical model of the FPI-OCMI system and the mechanism for the amplified sensitivity due to Vernier effect is presented. Numerical calculations are also performed to verify the analytical derivations.