How can I warp text or an object to a path?

I agree because I alwas prefer clean handmades instead of standard effects which everybody could do :-)

Darrius,

One important difference between handmade and (Envelope/whichever) Distort(ed)/Warp(ed) whatever is the, well, distortion, maybe especially noticeable in subtle details such as parallel and gentle rounding/thickness change.

Draw a shape, make on top of the text

Select them, Object> Envelop Distort> Make with Top Object.

Here is a really long and tedious way to do it.

Summary:

Convert all your letters to rectangles, cut the curve into the bottoms of the rectangles and envelope distort each letter.

Step-By-Step

This may not be perfect, but it might get you closer to what you want to do.

Hope this helps.

Darrius,

Such shapes are handmade. Smart Guides are your friends along with Ctrl/Cmd+Z.

In the case shown, the upper parts of the letters are unchanged, some of the lower parts are stretched..

To have the bottom part follow a path at a distance, you can start by selecting the path and then applying Object>Path>Offset Path to fit the lowest curve, then once more to fit the general thickness of the lower serifs.

To guide your stretching the straight parts downwards, you may use the Line (Segment) Tool to create guides crossing the offset paths; you can Direct Select relevant Anchor Points and ClickDrag them down to the intersections.

And so on, including actual (re)drawing.

For some non text objects, you can simply create the offset path running over the lower part(s), then select it and Object>Divide Objects Below and delete the cutoff(s).