Compiler Cost of searching wild char '%%' in like clause

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SQL

SQL-Server

I have a dynamic stored procedure and have to add where clause dynamically in case statement in SQL Server 2008.

My procedure is as below: -

CREATE PROCEDURE SPGETDATA
    @STRNAME NVARCHAR(100),
    @STRCODE NVARCHAR(100)
    
    AS
    BEGIN
    SELECT  myTable.*
    FROM myTable
    WHERE 
    IsDELETED = 0  
    AND STRNAME LIKE CASE WHEN (RTRIM(LTRIM(@STRNAME))) <> '' THEN 
    '%'+ @STRNAME + '%' ELSE '%%' END 
    AND STRCODE LIKE CASE WHEN (RTRIM(LTRIM(@STRCODE)) <> '') THEN 
    '%' + @STRCODE + '%'  ELSE '%%' END** 
    
    END

The user can select either @strname or @strcode. But not both at a time.

In that case one like statement is ok but the alternative is always a burden over query because it will always be as

@STRNAME like '%%'

or as below

@STRCODE like '%%'

Now if i use this approach, will compiler will cost some time to search like '%%' even there is nothing to match or it will bypass it and cost nothing. I checked the execution plan also but it displays nothing for the like clause.
Hence i have to use this in webApps so speed of the sp has to consider. And the table has millions of rows.

Any one who can help please?
Please help?