The 58-year-old man has been charged with making a statement or doing an act to create false apprehension as to the existence of a danger or threat.
The 52-year-old has been charged with making a threat to unlawfully do an act, possessing a prohibited drug and possessing drug paraphernalia.
Both men have been released on bail and are set to appear in the Rockingham Magistrates Court on April 7 and the Geraldton Magistrates Court on April 14.
Premier Mark McGowan revealed that he had received threats against both himself and his family in February of this year which he indicated was likely related to anti-vaxx mandate protests.
Mr McGowan was last year forced to close his electorate office after receiving death threats against himself and his staff over vaccination mandates.
Stay up-to-date on the latest news with Your Morning Agenda - supported by a network of local journalists from all major Australian cities, ensuing timely and first hand insights on local stories:
Download LiSTNR and enjoy a new world of audio. All your favourite shows and stations in one library.