  We develop a new method of modeling microlensing events based on a Monte
Carlo simulation that incorporates both a Galactic model and the constraints
imposed by the observed characteristics of the event. The method provides an
unbiased way to analyze the event especially when parameters are poorly
constrained by the observed lightcurve. We apply this method to search for
planetary companions of the lens in OGLE-2003-BLG-423, whose maximum
magnification A_max=256+-43 (or A_max=400+-115 from the lightcurve data alone)
is the highest among single-lens events ever recorded. The method permits us,
for the first time, to place constraints directly in the
planet-mass/projected-physical-separation plane rather than in the
mass-ratio/Einstein-radius plane as was done previously. For example,
Jupiter-mass companions of main-sequence stars at 2.5 AU are excluded with 80%
efficiency.
