I'm travelling, I won't make it on time.
'In viaggio' — in VIA-gio. Stress 'VIA'. The 'ggio' ending sounds like 'jo'.
Use when you are literally in transit and will not arrive on time for the plans. This is a factual, geographic impossibility — no one can argue with it.
'In viaggio' means 'travelling' or 'in transit'. 'Non arrivo in tempo' means 'I won't arrive on time'. Together they explain the situation factually and without excuse-making, which is appreciated.
Ho perso la coincidenza.
I missed my connection.
'Coincidenza' — connecting train/bus. Very credible on Italian rail networks
C'è traffico, ci metto ancora un'ora.
There's traffic, I'll take another hour.
For car journeys — Italian traffic (especially in Rome/Milan) is notorious
L'autostrada è bloccata.
The motorway is blocked.
Motorway closures due to accidents are common and generate immediate sympathy
The A1 (Autostrada del Sole) connecting Milan to Naples is one of Italy's busiest motorways and is famous for traffic and accidents, especially during holidays. Mentioning it immediately signals the severity of the delay.