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Choose a specific grid intersection at the centre of your space. If the centre of your space is a grid square (as it is for most PCs), pick one of its four corners.
edit: It looks to me as if emergency force sphere's 5' radius hemisphere centred on you places you in your choice of the four squares that the dome takes up.
looking at the templates online makes me laugh every time.....
if the spell is a 5' burst the template assumes Im standing on an intersection. I know things like "burst from you" are only flavor text but it never made much sense to me that I could send out a 5' burst that did not affect someone directly adjacent to me.
Assume a silly combat where Im completely surrounded by enemies:
x x x
x M x
x x x
I couldn't hit everyone with that 5' burst since Id need to pick a square so MAYBE could affect a few of them (in bold)
x x x
x M x
x x x
BUT if I had Whirlwind Attack in the same scenario they are all in reach so I could hit every one of them. Seems silly, I know, but in a game that uses squares and grids Im surprised that "5' radius spread from you" isn't the same as your 5' threat range with a melee weapon:
x x x
x M x
x x x
oh, I get the difference in how the rules are written.....I don't understand WHY they are written differently! FAQ already hit!!
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What Splendor said: Its a mechanic to make the game run easier.
However, that's why the game has GMs. Sometimes a GM just has to rule on something and it may not be entirely RAW. For example, if you wanted to cast emergency force sphere, BUT there is for some reason no grid intersection that would allow a legal 5' radius force sphere under the Wall of Force rules about being continuous and unbroken, but there is in fact a legal 5' radius that doesn't align with the grid intersections, the GM can simply allow the PC to cast the spell centered off the grid intersections in the legal space available.
I agree that it is not spelled out explicitly in the rules, but I think it's fairly clear by extension that it should operate as Starglim says - you pick a grid intersection in your space as the origin of the spell. That's certainly how I run it in my games. Here are the relevant rules (all from the Area section of Aiming a Spell):
Regardless of the shape of the area, you select the point where the spell originates, but otherwise you don't control which creatures or objects the spell affects. The point of origin of a spell is always a grid intersection.
Most spells that affect an area function as a burst, an emanation, or a spread. In each case, you select the spell's point of origin and measure its effect from that point.
An emanation spell functions like a burst spell, except that the effect continues to radiate from the point of origin for the duration of the spell. Most emanations are cones or spheres.
A cone-shaped spell shoots away from you in a quarter-circle in the direction you designate. It starts from any corner of your square and widens out as it goes.
A line-shaped spell shoots away from you in a line in the direction you designate. It starts from any corner of your square and extends to the limit of its range or until it strikes a barrier that blocks line of effect.
A sphere-shaped spell expands from its point of origin to fill a spherical area. Spheres may be bursts, emanations, or spreads.
From these rules, we know that a spell's point of origin is always a grid intersection. (This is shown in the Spell Areas diagram just above this section of the rules - note that the red dot is the point of origin, not the position of the caster). The rules also state that you choose the point of origin. Furthermore, it's clear how a cone-shaped emanation originating from you (such as detect secret doors) works - you pick a corner of your square as the origin. It's also clear how a line-shaped emanation originating from you (such as gust of wind) works - you pick a corner of your square as the origin. All that remains is for us to work out how a sphere-shaped emanation (such as antimagic field) centred on you works. Based on all this information, I contend that you should pick a corner of your square as its origin.
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Actually, the case that made me write this post was a GM that fumbled the emergency force sphere because I was in a 2x2 area and he ruled that as the sphere is centered on me it would take half a square of squares that were occupied.
Sounds like your GM was abrogating his role and being slavishly pedantic about following rules. Bottom line, there was enough space for the sphere to appear, the grid intersection rule is a convenience that the GM can overrule when appropriate, and he should let you cast the spell. I'm all for GM's making rulings, but I reserve the right to point out when they're being silly.