ABSTRACT Periodic quasars are candidates for binary supermassive black holes (BSBHs) efficiently emitting low-frequency gravitational waves. Recently, ∼150 candidates were identified from optical synoptic surveys. However, they may be false positives caused by stochastic quasar variability given the few cycles covered (typically 1.5). To independently test the binary hypothesis, we search for evidence of truncated or gapped circumbinary accretion discs (CBDs) in their spectral energy distributions (SEDs). Our work is motivated by CBD simulations that predict flux deficits as cut-offs from central cavities opened by secondaries or notches from minidiscs around both BHs. We find that candidate periodic quasars show SEDs similar to those of control quasars matched in redshift and luminosity. While seven of 138 candidates show a blue cut-off in the IR–optical–UV SED, six of which may represent CBDs with central cavities, the red SED fraction is similar to that in control quasars, suggesting no correlation between periodicity and SED anomaly. Alternatively, dust reddening may cause red SEDs. The fraction of extremely radio-loud quasars, e.g. blazars (with R > 100), is tentatively higher than that in control quasars (at 2.5σ). Our results suggest that, assuming most periodic candidates are robust, IR–optical–UV SEDs of CBDs are similar to those of accretion discs of single BHs, if the periodicity is driven by BSBHs; the higher blazar fraction may signal precessing radio jets. Alternatively, most current candidate periodic quasars identified from few-cycle light curves may be false positives. Their tentatively higher blazar fraction and lower Eddington ratios may both be caused by selection biases.