Which spells can stop a magic user from using a summoning spell either by stopping the spell effect or by stopping the magic user from casting?
I can only think of two: Counterspell and Anti-Magic Field
Are there any others?
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Adapted from this answer.
Make the enemy unable to cast spells
Animal Shapes (PHB, pg. 212) Requires willing target.
Antimagic Field (PHB, pg. 213) 10 foot sphere around your self, requires position management.
Feeblemind (PHB, pg. 239) Int save, resave after 30 days.
Mass Polymorph (XGtE, pg. 160) Wisdom save.
Polymorph (PHB, pg. 266) Wisdom save.
True Polymorph (PHB, pg. 283) Wisdom save.
Confusion (PHB, pg. 224) Wisdoms save, 20% chance to act normally even on a failed save.
Dominate Beast (PHB, pg. 234) Wisdom save. Requires beast creature type. The only beast with spellcasting I'm aware of is Traxigor, an archmage that was polymorphed into an otter from the adventure Descent into Avernus. Traxigor does not have any summoning spells on his statblock, but the DM may choose to put some there. This will also work on an 18th level NPC druid while in Wildshape form.
Dominate Monster (PHB, pg. 235) Wisdom save.
Dominate Person (PHB, pg. 235) Wisdom save, only works on humanoids.
Slow (PHB, pg. 277) Wisdom save, possibility for a single turn delay.
Sleep (PHB, pg. 276)
Imprisonment - Slumber (PHB, pg. 275) Wisdom save.
Hold Person (PHB, pg. 251) Wisdom save, requires humanoid.
Hold Monster (PHB, pg. 251) Wisdom save.
Power Word Stun (PHB, pg. 267) Target must have 150 or fewer hitpoints.
Psychic Scream (XGtE, pg. 163) Intelligence save.
Divine Word (PHB, pg. 234) Charisma save. 40 or fewer hit points, target is blinded. 30 or fewer, target is also stunned. 20 or fewer, target is dead.
Reality Break (EGtW, pg. 189) Wisdom save. 20% chance to stun, 20% chance to blind, 60% chance to take a lot of damage but still be able to act.
Contagion (PHB, pg. 227) Requires three failed Constitution saves. Inflicts a disease of your choice, three of which are applicable here.
Symbol (PHB, pg. 280) Lots of applicable options here.
Hypnotic Pattern (PHB, pg. 252) Wisdom save.
Tasha's Hideous Laughter (PHB, pg. 280) Wisdom save.
Modify Memory (PHB, pg. 261) Wisdom save.
Many of the conjure something spells require you to target an unoccupied space you can see, so inflicting the blindness condition with Blindness/Deafness (PHB, pg. 219) or Sunbeam (PHB, pg. 279) would do the trick if the summoning spell required sight. Additionally, Darkness (PHB, pg. 230), Fog cloud (PHB, pg. 243), and Cloudkill (PHB, pg. 222) would prevent the caster from seeing any unoccupied spaces within range.
All of the summoning spells have verbal components, so the Silence (PHB. pg. 275) will prevent them from being cast.
Leomund's Tiny Hut (PHB, pg. 255) If the caster is inside the hut, they cannot target a point outside the hut, and creatures summoned inside the hut cannot leave. Casting time of 1 minute and the hut is quite small.
Stopping their spell
Preventing Planar Travel
Mordenkainen's Private Sanctum (PHB, pg. 262) Casting time 10 minutes.
Forbiddance (PHB, pg. 243) Casting time 10 minutes
Sending the caster to another plane
Imprisonment - Hedged Prison (PHB, pg. 252)
Maze (PHB, pg. 258) Just works.
Banishing Smite (PHB, pg. 216) Damage must reduce target to 50 of fewr hit points.
Banishment (PHB, pg. 217) Charisma save.
Plane Shift (PHB, pg. 266) Must hit on a melee spell attack, and target must fail a Charisma save.
And finally, you can cast wish to cast any spell in this answer, or appeal to the DM with something like “I wish you wouldn’t do that.”
1 to equip them with armor they are not proficient in, if you accept "Would forcing armour on a wizard using an illusion spell and Illusory Reality 'harm' them?"