  Context. By now more than 300 planets transiting their host star have been
found, and much effort is being put into measuring the properties of each
system. Light curves of planetary transits often contain deviations from a
simple transit shape, and it is generally difficult to differentiate between
anomalies of astrophysical nature (e.g. starspots) and correlated noise due to
instrumental or atmospheric effects. Our solution is to observe transit events
simultaneously with two telescopes located at different observatories. Aims.
Using this observational strategy, we look for anomalies in the light curves of
two transiting planetary systems and accurately estimate their physical
parameters. Methods. We present the first photometric follow-up of the
transiting planet HAT-P-16 b, and new photometric observations of WASP-21 b,
obtained simultaneously with two medium-class telescopes located in different
countries, using the telescope defocussing technique. We modeled these and
other published data in order to estimate the physical parameters of the two
planetary systems. Results. The simultaneous observations did not highlight
particular features in the light curves, which is consistent with the low
activity levels of the two stars. For HAT-P-16, we calculated a new ephemeris
and found that the planet is 1.3 \sigma colder and smaller (Rb = 1.190 \pm
0.037 RJup) than the initial estimates, suggesting the presence of a massive
core. Our physical parameters for this system point towards a younger age than
previously thought. The results obtained for WASP-21 reveal lower values for
the mass and the density of the planet (by 1.0 \sigma and 1.4 \sigma
respectively) with respect to those found in the discovery paper, in agreement
with a subsequent study. We found no evidence of any transit timing variations
in either system.
