Julia Ward Howe, author most famously of the "Battle Hymn of the Republic," and Julia Wilbur didn't share much beyond their first name and pro-Union sentiments.

They were of the same generation--Howe was born in 1819, four years after Wilbur. But they traveled in very different circles. Howe grew up wealthy in New York City. She became further well-connected through marriage, when she wed Dr. Samuel Howe, the head of the Perkins Institution for the Blind in Boston. She socialized with fellow poets Longfellow and Whittier, wrote articles for the Atlantic Monthly, traveled to Europe. All this was far out of reach of her contemporary Julia Wilbur in upstate New York. (Howe's life was not as wonderful as it sounds--her husband was a dictator, she was frequently and unhappily pregnant.)

For Julia Wilbur, the abolitionist Senator Charles Sumner was someone to admire from afar. For Julia Ward Howe, Charles Sumner was her husband's (slightly weird) best friend. 

In the fall of 1861, the Howes visited Washington with a high-level delegation. Samuel had become a leader with the U.S. Sanitary Commission, the group formed to provide medical supplies and other relief to the overwhelmed army. He suggested his wife come along, almost as a lark. But as biographer Elaine Showalter writes of Julia Ward Howe in The Civil Wars of Julia Ward Howe:

Setting out as a woman with nothing to give and nothing to do, she would return as the author of the greatest American war anthem in history.

According to Showalter's account, Julia traveled out to Munson's Hill in Northern Virginia (now part of suburban DC).  As her small group returned to the Willard Hotel in Washington, they heard--and sang along with--troops, including those singing the already-famous tune and lyrics related to John Brown's body. That night she wrote her own words to the melody. She sent the poem to the editor of the Atlantic Monthly, a friend who had already published her work (again, being well-connected doesn't hurt). It grew in popularity, tremendously so.

Now...it turns out that Julia Ward Howe and Julia Wilbur did intersect at least once during the Civil War, in April 1863. When I read Showalter's book, I remembered that Julia Wilbur had written about her in her diaries, so went back to them.

On April 23, 1863:

This morning Mrs. Jacobs & myself went to Provost’s Office & got passes, & went to Washington on 10 A.M. boat. Mrs. J. was ordered out of neither ladies cabin or cars [which often happened to African American women]. We went directly to Willards & found Mr. Whipple in conference with Robert Dale Owen & Col. McKaye...Dr. S. G. Howe was ill & we did not see him, but we saw Mrs. Howe. They questioned Mr. Whipple, then myself. Mrs. J. endorsing what I said, & afterwards she gave some of her experience.

Howe, Owen, and McKaye were part of the American Freedmen's Inquiry Commission, authorized by Congress to investigate conditions of freedpeople in Union-occupied areas. While the report is riddled with prejudice, wittingly or not, it sounds like Julia, Harriet Jacobs, and J.W. Whipple, a missionary, made a convincing case. The AFIC report notes:

Sufficient evidence is before the Commission that colored refugees in general place a high value both on education for their children and religious instruction for themselves. In Alexandria and in various other places it came to the knowledge of the Commission that one of the first acts of the negroes when they found themselves free was to establish schools at their own expense; and in every instance where schools and churches have been provided for them they have shown lively gratitude and the greatest eagerness to avail themselves of such opportunities of improvement. 

It's not huge, but it's great to see how history collides! I'm also glad to see that our Alexandria contingent was not cowed by the relative fame of the visiting delegation.

After the war, Julia Wilbur heard Julia Ward Howe speak several times, although they eventually chose different sides of the suffrage divide.