Try searching for "@" with the double quotes.
I find the best way is to use a special-purpose script for finding email addresses. It's too much to expect the average user to enclose their search requests with quote marks.
#Allows the user to not have to worry about the @ symbol in email addresses acting as a wild card in Finds
Enter Find Mode [ ]
Show Custom Dialog [ Title: Get(ScriptName); Message: "Paste the email address you want to ﬁnd into the text box…"; Buttons:
“Find”; Input #1: OWN—contacts::email ]
If [ IsEmpty(OWN—contacts::email) ]
#Cancel if nothing entered
Enter Browse Mode
Exit Script [ ]
#Email address provided - put quotes around it so FileMaker can ﬁnd it easily
Set Field [ OWN—contacts::email; "\"" & OWN—contacts::email & "\"" ]
Perform Find [ ]
Thanks Nick and Matt! I ended up doing the script and tying it to a button "Find Email". I really appreciate your help. That issue really threw me after designing the database for hours.