Edit: rewritten the question, as I realised I wanted weak pullbacks, not comma objects.

Consider the 2-category $V$-$Cat$ of $V$-enriched categories. An example is $Cat$ itself, where we take $V=Cat$. I'm interested in the more general setting where $V$ is at least finitely complete and complete, if not possessing small limits and colimits outright. I also know that $V$ is such that small $V$-categories can be interpreted as categories internal to $V$ with object of objects given by a coproduct of the tensor unit.

Weak pullbacks exist in $Cat$, and can be calculated as a strict finite limit $A\times_C C^I \times_C B$ where $C^I$ is the isomorphism category of $C$. Actually I may not be interested in the weak pullbacks, but pseudo-pullbacks, depending on what this example in $Cat$ is.

Based on Finn's answer, I guess this may exist when cotensors by $I$ exist ($I$ is the groupoid with two objects $a,b$ with a unique isomorphism $a \stackrel{\sim}{\to} b$). So this then is my question:

When do weak/pseudo pullbacks (as appropriate) exist in $V$-$Cat$?