Small Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 4.7
Confusion; Situational Awareness
ATC Issue All Types; Airspace Violation All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Human Factors; Procedure
Aircraft X flying in to 36U from the south. Sector 32 called and said he was looking for the visual but if he didn't see the airport would execute an instrument approach procedure.  By Letter of Agreement (LOA) sector 3 has control for 36U landers from 32. I checked my Minimum Instrument Altitudes (MIA) in the area and thought 13;000 feet was a safe altitude.  It was for a time but the MIA creeps up to 13;900 feet.  I misinterpreted the MIA lines with sector lines and approach lines and thought 13;000 feet was a safe altitude until the MIA goes to 12;000 feet closer to the airport. The En-Route Minimum Safe Altitude Warning (EMSAW) alert didn't go off so I didn't question the safety of the flight since I already thought the Altitude was safe.Maybe reconsider EMSAW alerts procedures around landing airports. When a hard altitude entered would trigger the alert.
ZLC Controller describes a flight into an airport and is concerned about the Minimum IFR Altitudes (MIA) and altitude to assign the aircraft. Controller should have climbed the aircraft a thousand feet higher.