  We present milliarcsecond-resolution radio very long baseline interferometry
(VLBI) observations of the ultracool dwarfs TVLM513-46546 (M8.5) and 2MASS
J00361617+1821104 (L3.5) in an attempt to detect sub-stellar companions via
direct imaging or reflex motion. Both objects are known radio emitters with
strong evidence for periodic emission on timescales of about 2 and 3 hours,
respectively. Using the inner seven VLBA antennas, we detect unresolved
emission from TVLM513-46546 on a scale of 2.5 mas (~50 stellar radii), leading
to a direct limit on the radio emission brightness temperature of T_B > 4x10^5
K. However, with the higher spatial resolution afforded by the full VLBA we
find that the source appears to be marginally and asymmetrically resolved at a
low S/N ratio, possibly indicating that TVLM513-46546 is a binary with a
projected separation of ~1 mas (~20 stellar radii). Using the 7-hour baseline
of our observation we find no astrometric shift in the position of
TVLM513-46546, with a 3-sigma limit of about 0.6 mas. This is about 3 times
larger than expected for an equal mass companion with a few-hour orbital
period. Future monitoring of its position on a range of timescales will provide
the required astrometric sensitivity to detect a planetary companion with a
mass of ~10 M_J in a >15 d (>0.06 AU) orbit, or with a mass of ~2 M_J in an
orbit of >0.5 yr (>0.3 AU).
