The cavalry of Republican vice-presidential contenders and other party officials inside the courthouse for Donald J. Trump’s criminal trial was so large one day this week that the group initially had trouble arranging themselves in the two rows set aside for guests of the defense team.

Wedged into their seats, they were immediately confronted with testimony accusing their party’s leader — who was trying to inoculate his 2016 presidential campaign from political damage — of writing checks for bogus legal expenses to hide hush-money payments to a porn star.

None of the conservatives in the courtroom flinched or raised an eyebrow, including Gov. Doug Burgum of North Dakota and Representative Byron Donalds of Florida, both of whom are said to be under consideration for Mr. Trump’s running mate.

Instead, their stoic, protective presence underscored the biggest political quandary facing ambitious Republicans who want Mr. Trump to pick them for vice president: how to fiercely defend him without stealing any of his precious spotlight.

The prize for puzzling out the best approach could be a spot near the top of every ballot in the country this fall.

“He always wants killers out there fighting for him,” said Barry Bennett, a Republican strategist who advised Mr. Trump’s first presidential campaign. “But he also needs someone with experience and skills who can help shape his message, massage it and make it stronger.”