A multifrequency campaign on the BL Lac object PG 1553+113 was organized by the Whole Earth Blazar Telescope (WEBT) in 2013 April-August, involving 19 optical, two near-IR, and three radio telescopes. The aim was to study the source behaviour at low energies during and around the high-energy observations by the Major Atmospheric Gamma-ray Imaging Cherenkov telescopes in April-July. We also analyse the UV and X-ray data acquired by the Swift and XMM-Newton satellites in the same period. The WEBT and satellite observations allow us to detail the synchrotron emission bump in the source spectral energy distribution (SED). In the optical, we found a general bluer-when-brighter trend. The X-ray spectrum remained stable during 2013, but a comparison with previous observations suggests that it becomes harder when the X-ray flux increases. The long XMM-Newton exposure reveals a curved X-ray spectrum. In the SED, the XMM-Newton data show a hard near-UV spectrum, while Swift data display a softer shape that is confirmed by previous Hubble Space Telescope/Cosmic Origins Spectrograph and International Ultraviolet Explorer observations. Polynomial fits to the optical-X-ray SED show that the synchrotron peak likely lies in the 4-30 eV energy range, with a general shift towards higher frequencies for increasing X-ray brightness. However, the UV and X-ray spectra do not connect smoothly. Possible interpretations include: (i) orientation effects, (ii) additional absorption, (iii) multiple emission components, and (iv) a peculiar energy distribution of relativistic electrons. We discuss the first possibility in terms of an inhomogeneous helical jet model.