SECURE Water Amendments Act of 2014 - Amends the Omnibus Public Land Management Act of 2009 to: (1) include "planning for or addressing the impact of drought" among the activities for which the Secretary may make grants and enter cooperative agreements for water management improvement, (2) include Hawaii among the states in which eligible grant and agreement applicants may be located, (3) authorize appropriations for such grants and agreements, and (4) authorize appropriations for national water availability and use assessment program grants for FY2014-FY2018.