  The silver ruthenium oxide AgRuO$_3$ consists of honeycomb
[Ru$_2^{5+}$O$_6^{2-}$] layers, and can be considered an analogue of
SrRu$_2$O$_6$ with a different intercalation stage. We present measurements of
magnetic susceptibility and specific heat on AgRuO$_3$ single crystals which
reveal a sharp antiferromagnetic transition at 342(3)K. The electrical
transport in single crystals of AgRuO$_3$ is determined by a combination of
activated conduction over an intrinsic semiconducting gap of $\approx$ 100 meV
and carriers trapped and thermally released from defects. From powder neutron
diffraction data a N\'eel-type antiferromagnetic structure with the Ru moments
along the $c$ axis is derived. Raman and muon spin rotation spectroscopy
measurements on AgRuO$_3$ powder samples indicate a further weak phase
transition or a crossover in the temperature range 125-200 K. The transition
does not show up in magnetic susceptibility and its origin is argued to be
related to defects but cannot be fully clarified. The experimental findings are
complemented by DFT-based electronic structure calculations. It is found that
the magnetism in AgRuO$_3$ is similar to that of SrRu$_2$O$_6$, however with
stronger intralayer and weaker interlayer magnetic exchange interactions.
