When a long vowel has a meteg, there is a difference of opinion if the shva after it is na or nach. What about a short vowel with a meteg? Is it vayihi chen or vayhi chen? Is it tihiyeh or tihyeh? Is it vihiyitem or vihyitem? These words often sound more like a shva na, but the siddurim tend to have them as nach.
The opinion of the Minchat Shai (and most commentators, from what I can tell), is that a meteg on a short vowel in a closed syllable is almost always a euphonic meteg (there for stress or to stop you from swallowing a syllable, but not for the vowel quality), and thus does not affect the following shva. See also Geoffrey Khan's The Tiberian Pronunciation of Biblical Hebrew and The Pronunciation of the Verbs היה and חיה in the Tiberian Tradition of Biblical Hebrew.
There are two exceptions. Firstly, following a definite article prefix (הַ, בַּ, כַּ, לַ), we expect a dagesh chazak. In its absence, we often find a meteg with the patach to indicate that the schva should be na (eg. במסלה in Numbers 20:19). However, all other instances of patach with a meteg are short, and don't induce a following shva na. For example, in וידברו (Genesis 34:20) and ויהי־אור (Genesis 1:3), the shva on the yod is nach.
The second exception is not so much an exception, but a clarification that the vowel that looks short is actually long (ie. chirik missing its following yod or kubbuts instead of shuruk). For example, ויראו in Joshua 4:14 means they feared, not they saw, because of the meteg under the yod. However, the Minchat Shai explicitly says that יהיה, יחיה, להיות, לחיות all have shva nach. For להיות and יהיה and similar, my tikkun says to pronounce the ה as if there were a mappik, and that the shva is nach.
The only explicit dissenting opinion that I'm aware of is the author of Arugat HaBosem, who thinks that the meteg will lengthen the chirik in the verbs היה and חיה (and I imagine in all cases, but he's only quoted in this context). Jacobson's Chanting the Hebrew Bible also says that "some grammarians disagree with [the Minchat Shai]", but no further details are given.