Using multifrequency observations, from radio to gamma-rays of the blazar Mrk~501, we constructed their corresponding light curves and built periodograms using RobPer and Lomb-Scargle algorithms. Long-term variability was also studied using the power density spectrum and the detrended function analysis. Using the software VARTOOLS, we also computed the analysis of variance, box-least squares and discrete fourier transform. The result of these techniques showed an achromatic periodicity <~ 229 d. This, combined with the result of pink-color noise in the spectra, led us to propose that the periodicity was produced via a secondary eclipsing supermassive binary black hole orbiting the primary one locked inside the central engine of Mrk~501. We built a relativistic eclipsing model of this phenomenon using Jacobi elliptical functions, finding a periodic relativistic eclipse occurring every ~ 224 d in all the studied wavebands. This implies that the frequency of the emitted gravitational waves falls slightly above 0.1 mHz, well within the operational range of the upcoming LISA space-based interferometer, and as such, these gravitational waves must be considered as a prime science target for future LISA observations.