You wouldn’t believe how often I get asked this, in the comment-responses to my electronics videos. (I’ve just added this to my FAQ)
In the US, solder is pronounced “saw-der” (ˈsɑːdər) without the L. My family is Australian- I grew up doing electronics projects with my Dad, pronouncing it with the L as “sole-der” (ˈsɒldər). I have to really make an effort to say it the American way.
Here’s an interesting etymonline entry that shows the original mid 14th century word was “sawd” with no “L”. It seems unlikely that this is the reason Americans pronounce it without an “L”, but it’s as good an excuse as any
mid-14c., sawd, from Old French soldure, from solder “to join with solder,” from Latin solidare “to make solid,” from solidus “solid” (see solid). Modern form is from early 15c. The -l- still is sounded in Great Britain. Related: Soldered; soldering. The noun is first attested late 14c.
For reference, here is the entry for “solder” in the Oxford English Dictionary, including recordings. The pronunciation with the L is listed as British English, while the other is listed as American pronunciation.
And here’s a fun article about other words with missing L’s.