Shareholders made demands mostly around reducing carbon emissions, but the fireworks that lit up annual meetings last year were missing for ExxonMobil and Chevron Corp. 

Investors overall stuck with board recommendations at the two events in late May. However, there was more support for increased climate disclosures.

At the ExxonMobil annual meeting last week, 52% voted in favor of an audit to determine whether a target of net-zero global emissions by 2050 would affect the financial bottom line. Last year, a similar proposal was narrowly defeated by the ExxonMobil shareholders, with 49.4% in favor.

“We have opportunities to play a leading role in helping society achieve its net-zero ambitions and in meeting the world’s growing demand for energy and essential products,”...