Synonym for to make a pilgrimage?

Solution 1:

pilgrim = peregrine

Though Chaucer famously had his springtide folk “long to go on pilgrimages, and palmers to seek strange strands”, our common word pilgrim ultimately derives from Latin peregrīnus.

This same etymon has historically supplied us with a host of other, closely related terms which though less common today than they were of old, are still sometimes used — especially if you know some Romance or history.

So for example:

  • A pilgrim is a peregrine. (in English since the year 1395)
  • To go on a pilgrimage is to to peregrinate. (since 1593)
  • A pilgrimage is the same thing as a peregrination (since 1475) or the older and now-obsolete peregrinage. (since 1340)
  • If you worry that your peregrines might be confused for raptors, try the newer peregrinator instead. (since 1610)
  • Although peregrinity (since 1591) once meant a foreign journey, it now means foreignness if it means anything at all. It may be obsolete.
  • Peregrinancy (since 1674) once meant restlessness or inclination toward movement, but it too is now obsolete.

A recent OED citation for the verb peregrinate in the sense of “travels broadly” is used in a figurative sense:

  • 1996   Voice Lit. Suppl. (Nexis) 9 July 12
    He..peregrinates widely across cultural criticism and history to put Atlanta in context.

However, these are all fancy, learnèd terms, and you wouldn’t want to just plunk them down in any old bit of text.

Once you realize that pilgrim = peregrine, all else follows.

Solution 2:

The verb is the same as the noun, so if you go on a pilgrimage you are pilgrimaging.

See this entry at ODO.

So your sentence would be:

The text excludes the following people from the requirement to pilgrimage.

Solution 3:

The answer lies in your question.

Apart from using pilgrimage as a noun, you can also use it as a verb in accordance with the following definition:

  1. go on a pilgrimage

Usage examples:

  1. He pilgrimaged last year with his mother.

  2. Every year, Muslims pilgrimage with immense amount of religious passion.