Apologising
I'm afraid I offer/owe you an apology.
owe someone an apology
I'm afraid the problem couldn't be avoided/denied.
avoided
I hope you won't /shouldn't mind too much.
won't mind
I can/can't apologise enough for forget/forgetting your birthday
can't apologise enough
for forgetting
I can't get out of/away from going to my grandmother's party.
get out of
I hope you won't be terribly/completely disappointed.
terribly disappointed
I'm extremely/absolutely sorry for...
extremely sorry
I'm afraid the decision wasn't up/out of to me
up to
I hope it won't cause/put you any inconvenience.
cause someone inconvenience
I would/must apologise for...
must apologise
It isn't my fault/blame that I was late.
fault
I hope I haven't put /cause you to any inconvenience.
put someone to inconvenience
Please could you also make/give my apologies to (name of person).
give my apologies
Please accept my sincere/true apologies.
sincere apologies
Our warmest/kindest thoughts are with you as you recover from your accident.
warmest thoughts