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(abridged) Using the particularly long gravitational microlensing eventOGLE-2014-BLG-1186 with a time-scale $t_\mathrm{E}$ ~ 300 d, we present amethodology for identifying the nature of localised deviations from single-lenspoint-source light curves, which ensures that 1) the claimed signal issubstantially above the noise floor, 2) the inferred properties are robustlydetermined and their estimation not subject to confusion with systematic noisein the photometry, 3) there are no alternative viable solutions within themodel framework that might have been missed. Annual parallax and binarity couldbe separated and robustly measured from the wing and the peak data,respectively. We find matching model light curves that involve either a binarylens or a binary source. Our binary-lens models indicate a planet of mass $M_2$= (45 $\pm$ 9) $M_\oplus$, orbiting a star of mass $M_1$ = (0.35 $\pm$ 0.06)$M_\odot$, located at a distance $D_\mathrm{L}$ = (1.7 $\pm$ 0.3) kpc fromEarth, whereas our binary-source models suggest a brown-dwarf lens of $M$ =(0.046 $\pm$ 0.007) $M_\odot$, located at a distance $D_\mathrm{L}$ = (5.7$\pm$ 0.9) kpc, with the source potentially being a (partially) eclipsingbinary involving stars predicted to be of similar colour given the ratiosbetween the luminosities and radii. The ambiguity in the interpretation wouldbe resolved in favour of a lens binary by observing the luminous lens starseparating from the source at the predicted proper motion of $\mu$ = (1.6 $\pm$0.3) mas yr$^{-1}$, whereas it would be resolved in favour of a source binaryif the source could be shown to be a (partially) eclipsing binary matching theobtained model parameters. We experienced that close binary source stars pose achallenge for claiming the detection of planets by microlensing in events wherethe source passes very close to the lens star hosting the planet.

OGLE-2014-BLG-1186: gravitational microlensing providing evidence for a planet orbiting the foreground star or for a close binary source?