[sql-server] Trigger to fire only if a condition is met in SQL Server

The _ character is also a wildcard, BTW, but I'm not sure why this wasn't working for you:

CREATE TRIGGER 
    [dbo].[SystemParameterInsertUpdate]
ON 
    [dbo].[SystemParameter]
FOR INSERT, UPDATE 
AS
  BEGIN
    SET NOCOUNT ON
      INSERT INTO SystemParameterHistory 
      (
        Attribute,
        ParameterValue,
        ParameterDescription,
        ChangeDate
      )
    SELECT
      I.Attribute,
      I.ParameterValue,
      I.ParameterDescription,
      I.ChangeDate
    FROM Inserted AS I
    WHERE I.Attribute NOT LIKE 'NoHist[_]%'
END