The intensity of the geomagnetic field varies over different time-scales ranging from days to millions of years. Yet, limits for the maximum intensity of the field as well as for its maximum rate of change are poorly constrained due to inadequate temporal resolution and large uncertainties in the geomagnetic record. Here we present firm limits on these fundamental properties by constructing a high-resolution archaeointensity record of the Levant from the 11th century to the early 9th century BCE, a period over which the geomagnetic field reached its maximum intensity in Eurasia over the past 50000 years. We investigate a 14C-dated sequence of ten layers of slag material, which accumulated within an ancient industrial waste mound of an Iron-Age copper-smelting site in southern Israel. Depositional stratigraphy constrains relative ages of samples analyzed for paleointensity, and 14C dates from different horizons of the mound constrain the age of the whole sequence. The analysis yielded 35 paleointenisty data-points with accuracy better than 94%, covering a period of less than 350 years, most probably 200 years. We combine the new record with a previously published dataset, and construct a high-resolution quasi-continuous archaeointensity curve of the Levant. The curve displays two dramatic spikes in geomagnetic intensity, each corresponding to virtual axial dipole moment (VADM) in excess of 200 ZAm2. The geomagnetic spikes rise and fall over a period of less than 30 years and are associated with VADM fluctuations of at least 70 ZAm2. Thus, the Levantine archaeomagnetic record places new constraints on maximum geomagnetic intensity as well as for its rate of change.