Short answer. By making an offer of proof on the record. Rule 132, Section 40 provides that if the excluded evidence is oral, the offeror may state for the record the name and other personal circumstances of the witness and the substance of the proposed testimony. That statement, not the witness's actual answer, is what preserves the issue.
What the law says
If the evidence excluded is oral, the offeror may state for the record the name and other personal circumstances of the witness and the substance of the proposed testimony
Rule 132, Section 40 — Tender of excluded evidence. Read the full provision →
What the law says
If documents or things offered in evidence are excluded by the court, the offeror may have the same attached to or made part of the record
Rule 132, Section 40 — Tender of excluded evidence. Read the full provision →
What the rule provides for an excluded oral answer
Rule 132, Section 40 addresses exactly this problem: "If the evidence excluded is oral, the offeror may state for the record the name and other personal circumstances of the witness and the substance of the proposed testimony." When the judge will not let the witness answer, you are not simply left without a record — you are allowed to put the substance of what the witness would have said on the record yourself.
The parallel rule for documents and things
The same section states a similar rule for other kinds of excluded evidence: "If documents or things offered in evidence are excluded by the court, the offeror may have the same attached to or made part of the record." For a document, that means physically attaching it to the record. Testimony cannot be attached the same way, since it has not been given — which is why the rule provides a different mechanism, a stated description, for oral evidence specifically.
What your statement has to cover
For the oral-evidence route, the text names three specific things your statement should cover: the witness's "name and other personal circumstances," and "the substance of the proposed testimony." Naming who the witness is, along with the details that identify them, establishes who would have testified; describing the substance of the proposed testimony puts on record what that witness would have said, even though the judge would not let them say it out loud in court.
Why this matters for your appeal
An appellate court reviewing an exclusion of evidence needs to know what was excluded in order to decide whether excluding it was error, and whether that error mattered to the outcome. Without a stated offer under this section, there is nothing in the record showing what the witness would have said, which leaves an appellate court with no way to evaluate the ruling. Making this statement, on the record, at the time the exclusion happens, is what gives an appellate court something to actually review.