Run blkid in a root terminal to see all your partitions, inkl. swap, and their uuid.

Open /etc/fstab change to the right uuid's.
Open /etc/initramfs-tools/conf.d/resume and change to the right uuid [the / partition, I suppose [It's right in my case :-)]].

Rebuild initramfs.
Restart.

Does it have to be executable?

No, it does not.

Can we please see the full output of

# blkid
# update-initramfs -u -k all
cat /etc/{fstab,initramfs-tools/conf.d/resume}

The "#" symbol indicates that the command should be run with root privileges.

I already tried altering and removing the file

/etc/initramfs-tools/conf.d/resume

but this didn't help.

Removing the file won't work, you should tell us how you altered it.

This is the correct content if you don't want to use the swap to hibernate:

RESUME=none

EDIT: and rebuild the initramfs after you've changed the file:

# update-initramfs -u -k all

I have an installation which initially had swap but now doesn't have it anymore. Yet, the entries for suspend to ram are effective and lead to boot delays. The following message is repeated several times:

Begin: Running /scripts/local-block ... done.

After some seconds, it finally gives up:

Have up waiting for suspend/resume device

I already tried altering and removing the file

/etc/initramfs-tools/conf.d/resume

but this didn't help.

Thanks in advance for any ideas on how to solve this.