A theoretical study of a new type of surface electromagnetic wave sensor, similar to a surface plasmon resonance (SPR) sensor, which utilizes a one-dimensional photonic crystal (1DPhC) instead of a metal film, is presented. Replacing the metal film in the SPR sensor by the 1DPhC has number of advantages including physical and chemical robustness, enhanced sensitivity, etc. 1DPhCs can be engineered to exhibit metal-like optical properties over given frequency intervals. Equivalently, the optical response of the 1DPhC can be described by an effective dielectric constant with a negative real value that permits the 1DPhC to support surface electromagnetic waves at frequencies within the forbidden transmission band. In our theoretical study, the 1DPhC is represented by a multilayer interference filter and we model the response of the system comprising a BK7 prism/multilayer/analyte in a Kretschmann configuration. For the system under study we express the reflectances of p- and s-polarized waves as a function of angle of incidence on the prism. Dips in the reflectance spectra represent the coupling of light waves to surface modes and this can be confirmed by sensitivity to refractive index changes at the multilayer-analyte surface. The theoretical study is accompanied by experiment with some results for the BK7 prism/multilayer/analyte system in the Kretschmann configuration.