Methods for making a supported chromium catalyst are disclosed, and can comprise contacting a silica-coated alumina containing at least 30 wt. % silica with a chromium-containing compound in a liquid, drying, and calcining in an oxidizing atmosphere at a peak temperature of at least 650° C. to form the supported chromium catalyst. The supported chromium catalyst can contain from 0.01 to 20 wt. % chromium, and typically can have a pore volume from 0.5 to 2 mL/g and a BET surface area from 275 to 550 m2/g. The supported chromium catalyst subsequently can be used to polymerize olefins to produce, for example, ethylene-based homopolymers and copolymers having high molecular weights and broad molecular weight distributions.