One way to "sell" emergency management is via a risk management approach.
Many an emergency manager has struggled get attention to their program and the benefits it brings. One way to approach this is to align with your risk manager and change your target audience from some operational bureaucrat to bump it up to the policy level in your organization or jurisdiction.
Companies have boards of directors who can be risk averse and also comfortable managing risks. See this Uniting business continuity management and operational risk management, which might not be available to you, but likely not the only publication on the topic. Go search for similar titles and maybe get some ideas on how to highlight what your program brings to the table.
Brandon Greenberg shared the link above.