Equity markets are hitting new highs, signaling Wall Street is largely looking past the predictably volatile situation in Iran. That isn’t the case for individual companies.

As first-quarter report cards are rolling in, evidence is building that the war’s impact is stretching beyond the firms that move goods — and people — around the world. Most recently, the conflict raised costs for the container manufacturer Sonoco Products Co. and weighed on sales for industrial conglomerate Honeywell International Inc.