Context. Transition disks have large central cavities that have been resolved by imaging surveys during recent years. Cavities and other substructures in circumstellar disks are often interpreted as signposts to massive companions. Detecting companions at small angular separations is challenging with coronagraphic imaging observations. Aims. We aim to search for stellar and substellar companions in the central regions of transition disks. Such companions could be responsible for the large dust-depleted cavities. We want to determine if these disks might be circumbinary in their nature, similar to the HD 142527 system. Methods. We observed four systems, HD 100453, HD 100546, HD 135344 B, and PDS 70, with the sparse aperture masking mode of VLT/SPHERE, also leveraging the star-hopping method with the adaptive optics system. We extracted the complex visibilities and bispectra from the H2 and H3 imaging data. A binary model was fit to the closure phases to search for companions and estimate detection limits. For validation, we also analyzed four archival datasets of HD 142527 and inferred the orbital elements and atmospheric parameters of its low-mass stellar companion. Results. We have not detected any significant point sources in the four observed systems. With a contrast sensitivity of ≈0.004, we can rule out stellar companions down to ≈2 au and partially explore the substellar regime at separations ≳3–5 au. The analysis of HD 142527 B revealed that its projected orbit is aligned with dust features in the extended inner disk and that the mutual inclination with the outer disk is close to coplanar for one of the two solutions. Atmospheric modeling confirms the low-gravity and slightly reddened spectral appearance (T_eff ≈ 3300 K, log 𝑔 ≈ 3.7, and A_V ≈ 0.7). The inferred and derived bulk parameters (log L_*/L₀ ≈ −0.65, M_* ≈ 0.4 M_⊙, and R_* ≈ 1.46 R_⊙) are in agreement with dynamical constraints and evolutionary tracks. Conclusions. In contrast to HD 142527, we find no evidence that a close-in stellar companion is responsible for the resolved disk features of HD 100453, HD 100546, HD 135344 B, and PDS 70. Instead of a dynamical effect by a stellar companion, the formation of giant planets or even low-mass brown dwarfs could be shaping the innermost environment (≲20 au) of these circumstellar disks, as is the case with the planetary system of PDS 70.