This might have been "Microcosmic God" (1941) by Theodore Sturgeon. The Wikipedia article has a plot summary. In brief the main character, Kidder, is a biochemist who creates a small-sized species of intelligent beings who are short-lived and thus go through many generations in a short time thus leading to rapid development. These "Neoterics" develop many technologies which Kidder releases as his own inventions.
The story was included in several anthologies, particularly The Science Fiction Hall of Fame, Volume One (1970) which is where I first read it.
Mismatches: Kidder creates the Neoterics as a way to develop inventions beyond his own abilities, not out of boredom; The Neoterics are self-aware from a very early stage of their development. They worship Kidder as a divine being. The story is classed as a novelette by the ISFDB, and takes up some 25 pages in the 1970 ed. of The Science Fiction Hall of Fame, Volume One which might not count as "quite short".
The story does not end with the created species achieving intelligence. Indeed it almost starts there. Kidder takes it from protoplasm to self-aware intelligence.
This, then, was the answer to his problem. He couldn’t speed up mankind’s intellectual advancement enough to have it teach him the things his incredible mind yearned for. He couldn’t speed himself up. So he created a new race — a race which would develop and evolve so fast that it would surpass the civilization of man; and from them he would learn.
A relevant quote, supplied in a comment by DavidW and confirmed from the Internet Archive link supplied in a comment by user14111:
He got messing around with sisal fiber, found out how to fuse it, and boomed the banana industry by producing a practically unbreakable cord from the stuff.
You remember the popularizing demonstration he put on at Niagara, don’t you? That business of running a line of the new cord from bank to bank over the rapids and suspending a ten-ton truck from the middle of it by razor edges resting on the cord? That’s why ships now moor themselves with what looks like heaving line, no thicker than a lead pencil, that can be coiled on reels like garden hose.
The conclusion of the story is:
All this happened many years ago, and Kidder and Johansen may be alive today, and they may be dead. But that doesn’t matter too much. The important thing is that that great gray shell will bear watching. Men die, but races live. Some day the Neoterics, after innumerable generations of inconceivable advancement, will take down their shield.and come forth. When I think of that I feel frightened