Short answer. You choose. Section 1 lets you either complete the examination on other matters or adjourn it, then apply to the proper court where the deposition is being taken for an order compelling an answer; if the refusal was without substantial justification, the court can also make the refusing party or their counsel pay your reasonable expenses, including attorney's fees.
What the law says
If a party or other deponent refuses to answer any question upon oral examination, the examination may be completed on other matters or adjourned as the proponent of the question may prefer. The proponent may thereafter apply to the proper court of the place where the deposition is being taken, for an order to compel an answer.
Rule 29, Section 1 — Refusal to answer. Read the full provision →
Your options in the moment
You are not forced to either abandon the deposition altogether or halt everything the moment a refusal happens; the section explicitly lets the proponent of the question complete the examination on other matters, or adjourn the deposition entirely, whichever the proponent prefers, before ever needing to seek a court order compelling an answer. That flexibility means a single refusal doesn't have to derail the rest of the session.
Where to apply, and the scope beyond depositions
An application to compel an answer goes to the proper court of the place where the deposition is actually being taken, not necessarily the court where the underlying case is pending. The very same procedure for compelling an answer is also available when a party or witness refuses to answer any interrogatory submitted under Rule 23 or Rule 25, so the remedy isn't limited to oral depositions alone.
Cost-shifting cuts both ways
If the application is granted and the refusal was without substantial justification, the refusing party or counsel advising the refusal (or both) may be ordered to pay the proponent's reasonable expenses, including attorney's fees. But if the application is denied and found to have been filed without substantial justification, the proponent or their counsel can instead be made to pay the refusing party's expenses.
Why this two-way exposure matters
It discourages both frivolous refusals to answer and frivolous motions to compel, since either side risks bearing the other's costs depending on how the court ultimately rules on the application. A deponent who refuses to answer without a genuinely substantial justification risks paying the other side's expenses, while a party who runs to court over a refusal that had real merit risks paying the deponent's expenses instead — the exposure runs in both directions depending on who turns out to be right.