In three situations a stain does not receive the ordinary leniencies (the color of the surface, the surface's capacity to receive tum'ah). The reasoning is straightforward: in each of these three cases the woman may well have experienced a hargashah that was masked by other sensations. The likelihood that this is a Torah-level niddah is therefore higher, and we rule stringently.

1. A stain found immediately after urination

The source: Masechet Niddah 59b.

A woman should therefore take care to count 15 seconds from the end of urination before wiping. Some are stringent for 30 seconds. Then, if a stain is found, it can be handled under the ordinary leniencies. Another option is to train herself not to look at the toilet paper she wiped with.

A Sephardi woman need not wait before wiping. If she finds a stain on toilet paper immediately after urination, the stain is handled under the ordinary leniencies of a stain (so ruled Rav Ovadia Yosef).

2. A stain found after an object was inserted into the vagina

The source: Masechet Niddah 14a.

The most common example is a bedikah cloth. Even a tiny point of blood on a bedikah cloth that was inserted is therefore problematic.

Other examples:

The best course is to rinse or discard any such item without looking at it. A woman who is not in the seven clean days is not obligated to examine anything that was inserted. During the seven clean days, whether she must examine the item is a machloket; each woman should ask her rav.

If blood is found on an inserted object, the woman is a niddah unless the blood can be attributed to another source. If there is reason to think it is not uterine, ask. In any case of doubt, asking is better.

The husband as well

All of this applies to the husband's body after relations. So it's strongly recommended that he shower, or wipe himself with something black or red (or any dark color) on which stains do not show — and that he do so at least a few minutes after relations.

3. A stain found immediately after marital relations

The source: Masechet Niddah 14a.

A couple should therefore take care:

They should wait a few minutes. The sheets should be colored. Neither of them should go looking for stains.

If the couple does find a problematic stain immediately after relations, the woman is a niddah, and they should consult a rav before the next time they have relations, since it may have further halachic implications.

A note on the word "take care"

"Take care" here means a recommendation, not a technical obligation whose omission leaves you temei'ah. But it is a meaningful recommendation, and it prevents problems.