Breaks in the radio spectra of supernova remnants (SNRs) reflect the maximum energy of either shock-accelerated electrons or - in the case of pulsar wind nebulae - of electrons injected by the central pulsar. Otherwise, the break may result from energy losses due to synchrotron ageing or it is caused by energy-dependent diffusion. A spectral steepening of the plerionic SNR CTB87 at around 11 GHz was observed in the 1980s, but a recent analysis of CTB87's energetic properties based on new radio data raised doubt on it. CTB87 consists of a central compact component surrounded by a diffuse, centrally peaked, almost circular halo. Missing faint halo emission due to insufficient sensitivity of early high-frequency observations may be the reason for the reported spectral break. We intend to clarify the high-frequency spectrum of CTB87 by new sensitive observations. We used the broad-band 2-cm receiver at the Effelsberg 100-m telescope for sensitive continuum observations of CTB87 and its halo in two frequency bands. The new 2-cm maps of CTB87 show halo emission with a diameter of about 17' or 30pc for a distance 6.1 kpc in agreement with lower-frequency data. The measured flux densities are significantly higher than those reported earlier. The new 2-cm data establish the high-frequency continuation of CTB87's low-frequency spectrum. Any significant high-frequency spectral bend or break is constrained to frequencies well above about 18GHz. The extended halo of CTB87 has a faint counterpart in gamma-rays (VER J2016+37) and thus indicates a common origin of the emitting electrons.