Short answer. Yes. Where the court grants the motion to compel and finds the refusal was without substantial justification, the rule allows it to require the refusing party or deponent, or the counsel advising the refusal, or both, to pay the reasonable expenses of obtaining the order.
What the law says
it may require the refusing party or deponent or the counsel advising the refusal, or both of them, to pay the proponent the amount of the reasonable expenses incurred in obtaining the order, including attorney's fees
Rule 29, Section 1 — Refusal to answer. Read the full provision →
The rule reaches counsel personally
This is the striking feature of the provision, and it is stated without hedging. The exposure is not confined to the party or the deponent who stayed silent. It extends to the counsel advising the refusal, and the rule adds or both of them, so it is not a matter of choosing one target. A lawyer who instructs a witness not to answer is treated as an author of the refusal, not merely as a messenger for the client's position.
Two conditions have to be met
The sanction does not follow automatically from winning. First, the application must be granted — the court requires the refusing party or deponent to answer the question or interrogatory. Second, the court must also find that the refusal to answer was without substantial justification. That second finding is a separate step, and it is what protects a refusal made on a genuine ground. Being ordered to answer is therefore not the same as being ordered to pay.
What can be recovered
The measure is the reasonable expenses incurred in obtaining the order, including attorney's fees. Note what that is tied to: the cost of getting the order compelling an answer, not the cost of the litigation generally and not damages for the delay. The provision is aimed at putting the proponent back where it would have been had the answer simply been given, which is why keeping a clear record of what the motion actually cost is worth doing at the time.
The same exposure runs in your direction
Read the rest of the section before filing. If the application is denied and the court finds it was filed without substantial justification, it may require the proponent, or the counsel advising the filing, or both, to pay the refusing party's reasonable expenses including attorney's fees. The provision is symmetrical by design. It also covers refusals to answer interrogatories, not just questions on oral examination. Whether a particular refusal lacks substantial justification is a judgment worth making with your lawyer rather than in the heat of the deposition.