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We report on the inscription and characterization of narrow bandwidth fiber Bragg gratings (FBGs) with 850-nm resonance wavelength in polymer optical fibers (POFs). We use two fibers: an in-house fabricated microstructured POF (mPOF) with relative hole size of 0.5 and a commercial step-index POF, which supports six modes at 850 nm. The gratings have been written with the phase-mask technique and a 325-nm HeCd laser. The mPOF grating has a full-width at half-maximum (FWHM) bandwidth of 0.29 nm and the step-index POF has a bandwidth of 0.17 nm. For both fibers, the static tensile strain sensitivity is measured to be 0.71 pm/με at 850 nm and 1.3 pm/με at 1550 nm.