Yes, Glitterdust.
If the party doesn't have access to see invisibility, tremorsense, scent, or anything else to help pinpoint an invisible foe....depending on the arena size it might be hard for them to target the area for a Glitterdust burst where they -think- an Invisible mage might be hovering and whispering spells (is it an enclosed arena? How about an echo that could prevent pinpointing...) Though again, arena size depending, a sorcerer could spam it (maybe along with Widening it) and get lucky.
Summon Monster is close range, but it might still be hard to pinpoint by sound alone without a good "listener". In that case, Silence as previously suggested is a great idea for the not so obvious reasons - sure, it messes with PC casting but it keeps them from hearing you cast from your perch. I'd Widen it if you can (might be too high level for a henchman to pull off though.)
To further complicate things, you could Enlarge Spell so you can cast spells from farther away (making attempts to find you even more difficult) or Silent Spell if Silence isn't operating. That metamagic won't work well with Summons (cast times are atrocious), but if it keeps you undetected...
I had an "arena" style room once which had an enclosed hallway encircling the room about 3/4 of the way up the wall just below where the dome of the roof started to curve. There was a balcony concealed by an illusion running the entire circumference of the room and a hidden caster could see into the room and fire off spells.