Veils.

[Sanctaphrax]

You can also treat a veil as a straightforward block against attacks and other actions that require perception. That way, passive Alertness doesn't enter into it and no fancy rules interpretations are required.

[computerking]

You can also treat a veil as a straightforward block against attacks and other actions that require perception. That way, passive Alertness doesn't enter into it and no fancy rules interpretations are required.

That block could be broken with any Skill that requires perception, right? So swinging out blindly would be a valid attempt to break the block?

[Sanctaphrax]

Yeah.

[Tedronai]

A veil against any action which requires perception could be broken by perception.
Alertness is passive perception.
'Passive' in this instance means they don't need to take an action to roll it, and that they roll it reactively (don't have to even ask to roll it; it's the GM's responsibility to ask them to).
It would seem, then, that even an Alertness (passive) roll could break such a veil.

What is a fair frequency to use for giving opponents Alertness and/or Investigation checks? Which of these is how it should work?

1. Opponent gets an Alertness check (free action) the round the veiled character is in range to be observed.
2. Opponent gets an Alertness check (free action) *every* round the veiled character is in range to be observed.
3. Opponent gets an Alertness check (free action) the round the veiled character attacks the opponent.
4. Opponent gets an Alertness check (free action) the round the veiled character attacks anyone else in range to be observed.
5. Opponent may opt to take an Investigate check (regular action) the round the veiled character is in range to be observed.
6. Opponent may opt to take an Investigate check (regular action) the round the veiled character attacks the opponent .
7. Opponent may opt to take an Investigate check (regular action) the round the veiled character attacks anyone else in range to be observed.
8. Additional rules?

Options 5-7, if implemented in the absence of some variation of 1-4, would severely hamstring the Alertness skill.
Personally, I would suggest an Alertness roll the first time the veiled character is in range to be observed, and again whenever an occurrence would make that character more obvious to observers (anything from physical attacks, offensive blocks, and most offensive maneuvers to having the narration of their movement take them in front of that giant spotlight so that they're temporarily silhouetted)
As for Investigate checks, the character gets those whenever the player asks for them and spends an appropriate action (possibly standard, possibly supplemental, depending on context).

[UmbraLux]

You can also treat a veil as a straightforward block against attacks and other actions that require perception. That way, passive Alertness doesn't enter into it and no fancy rules interpretations are required.

This. 

What is a fair frequency to use for giving opponents Alertness and/or Investigation checks? Which of these is how it should work?

1. Opponent gets an Alertness check (free action) the round the veiled character is in range to be observed.
5. Opponent may opt to take an Investigate check (regular action)...<anytime they have an action and wish to so so - standard modifiers are applied>

Either or both of the above also work.

[polkaneverdies]

Tedronai nailed it.

[Becq]

Given that the block rules in general allow any (appropriate) skill to be used to break the block, and since a veil is a block is a block, I'd favor Sanctaphrax's suggestion.  So an attacker could swing wildly where he thought the invisible target was, and if he was very lucky (ie, beat the block) then he'd hit.  Possibly just barely, due to the block, but enough to cancel the veil.  (This assumes, of course, that the character has reason to believe there is someone within range of his attack.)

[sinker]

To be honest I do dislike that idea a little bit, but only from a thematic point of view. Consider that under that method, a blind and deaf world class fencer is more likely to hit than a very alert but only moderately trained swordsman. That seems a little off to me.

[computerking]

To be honest I do dislike that idea a little bit, but only from a thematic point of view. Consider that under that method, a blind and deaf world class fencer is more likely to hit than a very alert but only moderately trained swordsman. That seems a little off to me.

Oh, my, the scene you just created in my mind....

The PC's are quietly ushered into the Master of the house's exercise room, where 2 men are facing off in full fencing garb. One is in perfect stance, advancing and retreating with fluid grace, his opponent visibly less skilled with a sword, trying his best. After several  unsuccessful attempts to score a hit on his more competent opponent, the underdog is double-feinted, lured into an off-balanced strike, and defeated with a quick riposte and hit to the heart. The men lower their swords and bow to each other. The men take off their helmets, then the victor takes off his blindfold. "Perhaps Next time, James," He says, then turns to the PC's. "Oh, I didn't expect you this early. I'd heard you wanted to speak with me..."

I have to use that. Thank you, sinker!

[UmbraLux]

To be honest I do dislike that idea a little bit, but only from a thematic point of view. Consider that under that method, a blind and deaf world class fencer is more likely to hit than a very alert but only moderately trained swordsman. That seems a little off to me.

Only if the GM fails.  Modifiers still exist in FATE and, even if you play with aspects only, both blind and deaf should be aspects which easily help the defense if they don't simply get compelled to make the scene ludicrous.  (Absent some compensating power of course.)

[Becq]

From a game balance perspective, I can't help but wonder why someone who themes their block spell as affecting perception should have significantly more bang-for-the-buck than one who themese their block spell as impairing movement (paralysis, say -- or entangle).  Better to use the same mechanics for all blocks.

From a flavor text perspective, I would actually say that it makes some sense that someone who is skilled at creating a web of steel (and perhaps also at predicting an opponent's moves) might be as equipped to happen across an invisible target than someone who's just looking around for signs of his passage.

In any case, keep in mind that the veil is still a block, and as such still reduces (greatly) the likelihood of hitting, and the strength of the hit if one occurs.