Microorganisms present within a plurality of microorganism clusters immobilized in a porous support material may collectively define a supported bio-catalyst. When the microorganisms are effective to convert methane into one or more oxidized carbon compounds (e.g., methanotrophic bacteria), the supported bio-catalysts may be utilized to remove methane from methane-containing gas streams, such as those obtained from mining ventilation. Methods for processing a methane-containing gas stream may comprise interacting the gas stream with the supported bio-catalyst in substantial absence of a liquid phase, and obtaining a methane-depleted gas stream downstream from the supported bio-catalyst. Systems for processing a methane-containing gas stream may comprise the supported bio-catalysts housed in one or more vessels fluidly coupled to a source of methane-containing gas stream. A gas concentration in the methane-containing gas stream and/or the methane-depleted gas stream may be used to determine a current state or anticipated remaining lifetime of the supported bio-catalyst.